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Algebra Universalis最新文献

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The pairwise distributive law of semilattice congruences 半格同余的成对分配律
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-08-19 DOI: 10.1007/s00012-026-00942-x
Fernando Martin-Maroto, Antonio Ricciardo, Gonzalo G. de Polavieja
{"title":"The pairwise distributive law of semilattice congruences","authors":"Fernando Martin-Maroto,&nbsp;Antonio Ricciardo,&nbsp;Gonzalo G. de Polavieja","doi":"10.1007/s00012-026-00942-x","DOIUrl":"10.1007/s00012-026-00942-x","url":null,"abstract":"<div><p>We show that the congruence lattice of a semilattice satisfies a form of distributivity relative to principal congruences of the form <span>( Theta _{t odot s, s}.)</span> Particularly, we establish that semilattice congruences obey the “pairwise distributive law”: </p><div><div><span>$$ (cap _{i in w} Omega _{i}) vee Theta _{t odot s, s} = cap _{k,r in w} big ( (Omega _{k} cap Omega _{r}) vee Theta _{t odot s, s} big ) $$</span></div></div><p>for any two elements <i>t</i> and <i>s</i> and any family of congruences <span>({ Omega _{i}: iin w },)</span> with <i>w</i> a possibly infinite set.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00942-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decomposition of ideals in L-algebras l -代数的理想分解
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-08-19 DOI: 10.1007/s00012-026-00943-w
Simin Saidi Goraghani, Rajab Ali Borzooei
{"title":"Decomposition of ideals in L-algebras","authors":"Simin Saidi Goraghani,&nbsp;Rajab Ali Borzooei","doi":"10.1007/s00012-026-00943-w","DOIUrl":"10.1007/s00012-026-00943-w","url":null,"abstract":"<div><p>In this paper, by introducing irreducible ideals, we prove that any ideal of an <i>L</i>-algebra can be represented by an intersection of minimal irreducible ideals. Then we characterize the elements of the ideal generated by a set in the <i>L</i>-algebras, and obtain some related results. With those results, we prove that in <i>CL</i>-algebra <i>L</i> the representation of distinct minimal irreducible ideals of <i>L</i> is unique. Next, we verify the relationship between irreducible ideals and prime ideals of <i>L</i>-algebras. Then we define the radical of ideals in <i>L</i>-algebras, characterize the elements of it, and verify some of its properties. In the following, we present the definitions of primary ideals, primary decomposition of ideals and reduced primary decomposition of ideals in <i>L</i>-algebras, and study some of their basic properties. Finally, we verify some conditions that an ideal can have a reduced primary decomposition.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transfer of properties between a truncated Riesz space and its unitization 截断Riesz空间及其统一之间的性质转移
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-08-12 DOI: 10.1007/s00012-026-00945-8
Mohamed Habibi, Hamza Hafsi
{"title":"Transfer of properties between a truncated Riesz space and its unitization","authors":"Mohamed Habibi,&nbsp;Hamza Hafsi","doi":"10.1007/s00012-026-00945-8","DOIUrl":"10.1007/s00012-026-00945-8","url":null,"abstract":"<div><p>We study the transfer of fundamental order and completeness properties between a truncated Riesz space and its Alexandroff unitization. In particular, we distinguish genuine completeness notions, including relatively uniform completeness, Dedekind completeness, lateral completeness, universal completeness, and the (principal) projection property, from order-theoretic properties such as the Archimedean property. We establish characterizations and equivalences for several of these notions and provide counterexamples to highlight the necessity of certain assumptions and the independence of different completeness properties.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On hollowness in multiplicative lattices 关于乘法格中的空性
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-08-07 DOI: 10.1007/s00012-026-00941-y
Amartya Goswami, Joseph Zelezniak
{"title":"On hollowness in multiplicative lattices","authors":"Amartya Goswami,&nbsp;Joseph Zelezniak","doi":"10.1007/s00012-026-00941-y","DOIUrl":"10.1007/s00012-026-00941-y","url":null,"abstract":"<div><p>We extend strongly hollow and completely strongly hollow ideals from commutative rings to multiplicative lattices. We characterize these elements through residuals and localizations at maximal elements, and study them in semisimple, Gelfand, Prüfer, and weak <i>r</i>-lattices. Applications include criteria for quasi-locality, descriptions in weak Noether lattices, and representations of multiplicative lattices by completely strongly hollow elements.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00941-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tensor product in the category of effect algebras 效应代数范畴中的张量积
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-06-17 DOI: 10.1007/s00012-026-00938-7
Dominik Lachman
{"title":"Tensor product in the category of effect algebras","authors":"Dominik Lachman","doi":"10.1007/s00012-026-00938-7","DOIUrl":"10.1007/s00012-026-00938-7","url":null,"abstract":"<div><p>We study a tensor product in the category of effect algebras and in the category of partially ordered Abelian groups with order unit. We show that the tensor product preserves all the constructions that are essentially colimits over a connected diagram. Further, we prove the construction of a universal group for an effect algebra preserves all tensor products. We establish the corresponding functor from the category of effect algebras to the category of unital Abelian po-groups as a strong monoidal functor. We note that the technique we use in establishing the result could be used in various similar situations. Finally, we show that the tensor product of effect algebras does not preserve the Riesz decomposition property, which was an open question for a while.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00938-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reflexive digraphs in Taylor varieties 泰勒变体中的自反有向图
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-06-15 DOI: 10.1007/s00012-026-00936-9
Gergő Gyenizse, Miklós Maróti, László Zádori
{"title":"Reflexive digraphs in Taylor varieties","authors":"Gergő Gyenizse,&nbsp;Miklós Maróti,&nbsp;László Zádori","doi":"10.1007/s00012-026-00936-9","DOIUrl":"10.1007/s00012-026-00936-9","url":null,"abstract":"<div><p>We prove that a variety <span>(mathcal {V})</span> is a Taylor variety if and only if the compatible reflexive antisymmetric digraphs in <span>(mathcal {V})</span> are cycle-free.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00936-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the variety generated by all semirings of order two 关于所有二阶半环所产生的变化
IF 0.4 4区 数学
Algebra Universalis Pub Date : 2026-06-15 DOI: 10.1007/s00012-026-00937-8
Aifa Wang, Lili Wang, Peng Li, Qingrui Yin
{"title":"On the variety generated by all semirings of order two","authors":"Aifa Wang,&nbsp;Lili Wang,&nbsp;Peng Li,&nbsp;Qingrui Yin","doi":"10.1007/s00012-026-00937-8","DOIUrl":"10.1007/s00012-026-00937-8","url":null,"abstract":"<div><p>There are ten distinct two-element semirings up to isomorphism, denoted <span>( L_2, R_2, M_2, D_2, N_2, T_2, Z_2, W_2, Z_7 )</span>, and <span>( Z_8 )</span> in Bashir and Kepka (2007). Among these, the multiplicative reductions of <span>( M_2, D_2, W_2 )</span>, and <span>( Z_8 )</span> form semilattices, while the additive reductions of <span>( L_2, R_2, M_2, )</span> <span>( D_2, N_2 )</span>, and <span>( T_2 )</span> are idempotent semilattices, commonly referred to as <i>idempotent semirings</i>. Vechtomov and Petrov (2015) studied the variety generated by <span>( M_2, D_2, W_2 )</span>, and <span>( Z_8 )</span>, proving that it is finitely based, while Shao and Ren (2015) examined the variety generated by the six idempotent semirings, demonstrating that every subvariety of this variety is finitely based. This paper systematically investigates the variety generated by all ten two-element semirings. We prove that this variety contains exactly 480 subvarieties, each of which is finitely based.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unicoherence in locales 区域设置的一致性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-06-05 DOI: 10.1007/s00012-026-00933-y
Elena Caviglia, Luca Mesiti, Cerene Rathilal
{"title":"Unicoherence in locales","authors":"Elena Caviglia,&nbsp;Luca Mesiti,&nbsp;Cerene Rathilal","doi":"10.1007/s00012-026-00933-y","DOIUrl":"10.1007/s00012-026-00933-y","url":null,"abstract":"<div><p>In this paper, we generalize the concept of unicoherence to the context of frames. Unicoherence, originally introduced by Kuratowski, is a connectedness property that is well studied in classical topology and used to detect holes of a space. We extend the notion of unicoherence to locales and we then investigate its properties. In particular, we prove that many of the known characterizations of unicoherence for topological spaces extend to the setting of locales. Some of these characterizations interestingly involve separation properties for locales.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00933-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extension of (mathcal {F})-limits to general set families in the prime spectrum of a commutative ring 交换环素谱上广义集族(mathcal {F}) -极限的推广
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-05-26 DOI: 10.1007/s00012-026-00929-8
Oudika Ayoub, Mouadi Hassan, Driss Karim
{"title":"Extension of (mathcal {F})-limits to general set families in the prime spectrum of a commutative ring","authors":"Oudika Ayoub,&nbsp;Mouadi Hassan,&nbsp;Driss Karim","doi":"10.1007/s00012-026-00929-8","DOIUrl":"10.1007/s00012-026-00929-8","url":null,"abstract":"<div><p>We generalize the notion of the <span>(mathscr {F})</span>-limit, initially introduced by Garcia–Ferreira and Ruza–Montilla, to any infinite index set <i>I</i> together with a family <span>(mathscr {F}_{kappa }(I))</span> of subsets of <i>I</i> that need not be an ultrafilter. This extension permits the definition of a topology on <span>(textrm{Spec}(R))</span>, called the <span>(mathscr {F}_{kappa }(I))</span>-<i>limit topology</i>, whose topological properties we study in detail.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The four uniform completions of a unital archimedean vector lattice 一元阿基米德向量格的四个一致补全
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-05-11 DOI: 10.1007/s00012-026-00931-0
Richard N. Ball, Anthony W. Hager
{"title":"The four uniform completions of a unital archimedean vector lattice","authors":"Richard N. Ball,&nbsp;Anthony W. Hager","doi":"10.1007/s00012-026-00931-0","DOIUrl":"10.1007/s00012-026-00931-0","url":null,"abstract":"<div><p>In the category <span>(textbf{V})</span> of unital archimedean vector lattices, several relatively recent results have brought closure to the notion of uniform completion: there are exactly four constructs worthy of the name uniform completion. In all cases completeness requires the convergence of uniformly Cauchy sequences; the completions are distinguished by the manner in which the convergence is regulated.</p><ul>\u0000 <li>\u0000 <p>Ordinary uniform convergence is regulated by the canonical unit 1.</p>\u0000 </li>\u0000 <li>\u0000 <p>Inner relative uniform convergence, here termed <i>iru-convergence</i>, is regulated by an arbitrary positive element.</p>\u0000 </li>\u0000 <li>\u0000 <p>Outer relative uniform convergence, here termed <i>oru-convergence</i>, is regulated by an arbitrary positive element of a vector lattice containing the given object as a sub-vector lattice.</p>\u0000 </li>\u0000 <li>\u0000 <p><span>(*)</span>-<i>convergence</i> is equivalent to ordinary uniform convergence on certain specified quotients of the vector lattice.</p>\u0000 </li>\u0000 </ul><p> In each case the complete objects form a full monoreflective subcategory of <span>(textbf{V})</span>, denoted respectively <span>(textbf{ucV})</span>, <span>(textbf{irucV})</span>, <span>(textbf{orucV})</span>, and <span>(mathbf {*cV})</span>. In this article we survey these completions, comparing and contrasting them by means of a novel pointfree variant of the classical Yosida adjunction.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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