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Algebra Universalis最新文献

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Right-preordered groups from a categorical perspective
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-03-25 DOI: 10.1007/s00012-025-00886-8
Maria Manuel Clementino, Andrea Montoli
{"title":"Right-preordered groups from a categorical perspective","authors":"Maria Manuel Clementino,&nbsp;Andrea Montoli","doi":"10.1007/s00012-025-00886-8","DOIUrl":"10.1007/s00012-025-00886-8","url":null,"abstract":"<div><p>We study categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, studying some exactness properties, and showing that it is a quasivariety. We show that, from an algebraic point of view, the category of right-preordered groups shares several properties with the one of monoids. Moreover, we describe split extensions of right-preordered groups, showing in particular that semidirect products of ordered groups always have a natural right-preorder.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698528","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
Reorienting quandle orbits 调整烛台轨道的方向
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-03-25 DOI: 10.1007/s00012-025-00883-x
Lorenzo Traldi
{"title":"Reorienting quandle orbits","authors":"Lorenzo Traldi","doi":"10.1007/s00012-025-00883-x","DOIUrl":"10.1007/s00012-025-00883-x","url":null,"abstract":"<div><p>Motivated by knot theory, it is natural to define the orienta-tion-reversal of a quandle orbit by inverting all the translations given by elements of that orbit. In this short note we observe that this natural notion is unsuited to medial quandles.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00883-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698529","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
Characterizations of U-frames and frames that are finitely a U-frame
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-03-25 DOI: 10.1007/s00012-025-00888-6
Batsile Tlharesakgosi
{"title":"Characterizations of U-frames and frames that are finitely a U-frame","authors":"Batsile Tlharesakgosi","doi":"10.1007/s00012-025-00888-6","DOIUrl":"10.1007/s00012-025-00888-6","url":null,"abstract":"<div><p>In this article, we give algebraic characterizations of <i>U</i>-frames in terms of ring-theoretic properties of the ring <span>(mathcal {R}L)</span> of real-valued continuous functions on a completely regular frame <i>L</i>. We show that a frame is a <i>U</i>-frame if and only if it is an <i>F</i>-frame and its Čech–Stone compactification is zero-dimensional. We will also introduce frames that are finitely a <i>U</i>-frame and we will characterize them in terms of ring-theoretic properties in <span>(mathcal {R}L)</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00888-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698527","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
Correction: Projectivity in (bounded) commutative integral residuated lattices 修正：（有界）交换积分残差格中的投影
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-01-04 DOI: 10.1007/s00012-024-00879-z
Paolo Aglianò, Sara Ugolini
{"title":"Correction: Projectivity in (bounded) commutative integral residuated lattices","authors":"Paolo Aglianò,&nbsp;Sara Ugolini","doi":"10.1007/s00012-024-00879-z","DOIUrl":"10.1007/s00012-024-00879-z","url":null,"abstract":"","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00879-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925585","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
Algebraic frames in Priestley duality Priestley对偶中的代数框架
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-30 DOI: 10.1007/s00012-024-00876-2
Guram Bezhanishvili, Sebastian D. Melzer
{"title":"Algebraic frames in Priestley duality","authors":"Guram Bezhanishvili,&nbsp;Sebastian D. Melzer","doi":"10.1007/s00012-024-00876-2","DOIUrl":"10.1007/s00012-024-00876-2","url":null,"abstract":"<div><p>We characterize Priestley spaces of algebraic, arithmetic, coherent, and Stone frames. As a corollary, we derive the well-known dual equivalences in pointfree topology involving various categories of algebraic frames.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890063","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
A finite representation of relation algebra (varvec{1896_{3013}}) 关系代数的有限表示 (varvec{1896_{3013}})
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-30 DOI: 10.1007/s00012-024-00881-5
Jeremy F. Alm
{"title":"A finite representation of relation algebra (varvec{1896_{3013}})","authors":"Jeremy F. Alm","doi":"10.1007/s00012-024-00881-5","DOIUrl":"10.1007/s00012-024-00881-5","url":null,"abstract":"<div><p>We give a representation of relation algebra <span>(1896_{3013})</span>, which has symmetric atoms <span>(1')</span>, <i>a</i>, <i>b</i>, <i>c</i>, and <i>d</i>. The sole forbidden diversity cycle is <i>bcd</i>; the atom <i>a</i> is flexible. We give a group representation over <span>(mathbb {Z}/1531mathbb {Z})</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890046","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 z-elements of multiplicative lattices 在乘法格的z元素上
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-28 DOI: 10.1007/s00012-024-00882-4
Amartya Goswami, Themba Dube
{"title":"On z-elements of multiplicative lattices","authors":"Amartya Goswami,&nbsp;Themba Dube","doi":"10.1007/s00012-024-00882-4","DOIUrl":"10.1007/s00012-024-00882-4","url":null,"abstract":"<div><p>The aim of this paper is to investigate further properties of <i>z</i>-elements in multiplicative lattices. We utilize <i>z</i>-closure operators to extend several properties of <i>z</i>-ideals to <i>z</i>-elements and introduce various distinguished subclasses of <i>z</i>-elements, such as <i>z</i>-prime, <i>z</i>-semiprime, <i>z</i>-primary, <i>z</i>-irreducible, and <i>z</i>-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where <i>z</i>-elements are closed under finite products and a representation of <i>z</i>-elements in terms of <i>z</i>-irreducible elements in <i>z</i>-Noetherian multiplicative lattices.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00882-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890032","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 complete lattices of radical submodules and ( z )-submodules 关于根子模和( z ) -子模的完全格
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-13 DOI: 10.1007/s00012-024-00880-6
Hosein Fazaeli Moghimi, Seyedeh Fatemeh Mohebian
{"title":"On complete lattices of radical submodules and ( z )-submodules","authors":"Hosein Fazaeli Moghimi,&nbsp;Seyedeh Fatemeh Mohebian","doi":"10.1007/s00012-024-00880-6","DOIUrl":"10.1007/s00012-024-00880-6","url":null,"abstract":"<div><p>Let <i>M</i> be a module over a commutative ring <i>R</i>, and <span>(mathcal {R}(_{R}M))</span> denote the complete lattice of radical submodules of <i>M</i>. It is shown that if <i>M</i> is a multiplication <i>R</i>-module, then <span>(mathcal {R}(_{R}M))</span> is a frame. In particular, if <i>M</i> is a finitely generated multiplication <i>R</i>-module, then <span>(mathcal {R}(_{R}M))</span> is a coherent frame and if, in addition, <i>M</i> is faithful, then the assignment <span>(Nmapsto (N:M)_{ z })</span> defines a coherent map from <span>(mathcal {R}(_{R}M))</span> to the coherent frame <span>(mathcal {Z}(_{R}R))</span> of <span>( z )</span>-ideals of <i>R</i>. As a generalization of <span>( z )</span>-ideals, a proper submodule <i>N</i> of <i>M</i> is called a <span>( z )</span>-submodule of <i>M</i> if for any <span>(xin M)</span> and <span>(yin N)</span> such that every maximal submodule of <i>M</i> containing <i>y</i> also contains <i>x</i>, then <span>(xin N)</span>. The set of <span>( z )</span>-submodules of <i>M</i>, denoted <span>(mathcal {Z}(_{R}M))</span>, forms a complete lattice with respect to the order of inclusion. It is shown that if <i>M</i> is a finitely generated faithful multiplication <i>R</i>-module, then <span>(mathcal {Z}(_{R}M))</span> is a coherent frame and the assignment <span>(Nmapsto N_{ z })</span> (where <span>(N_{ z })</span> is the intersection of all <span>( z )</span>-submodules of <i>M</i> containing <i>N</i>) is a surjective coherent map from <span>(mathcal {R}(_{R}M))</span> to <span>(mathcal {Z}(_{R}M))</span>. In particular, in this case, <span>(mathcal {R}(_{R}M))</span> is a normal frame if and only if <span>(mathcal {Z}(_{R}M))</span> is a normal frame.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821130","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
Near-unanimity-closed minions of Boolean functions 布尔函数的近乎一致封闭的爪牙
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-11-20 DOI: 10.1007/s00012-024-00872-6
Erkko Lehtonen
{"title":"Near-unanimity-closed minions of Boolean functions","authors":"Erkko Lehtonen","doi":"10.1007/s00012-024-00872-6","DOIUrl":"10.1007/s00012-024-00872-6","url":null,"abstract":"<div><p>The near-unanimity-closed minions of Boolean functions, i.e., the clonoids whose target algebra contains a near-unanimity function, are completely described. The key concept towards this result is the minorant-minor partial order and its order ideals.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672559","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
Multisorted Boolean clones determined by binary relations up to minion homomorphisms 由二元关系决定的多分类布尔克隆，直至奴仆同态
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-11-06 DOI: 10.1007/s00012-024-00878-0
Libor Barto, Maryia Kapytka
{"title":"Multisorted Boolean clones determined by binary relations up to minion homomorphisms","authors":"Libor Barto,&nbsp;Maryia Kapytka","doi":"10.1007/s00012-024-00878-0","DOIUrl":"10.1007/s00012-024-00878-0","url":null,"abstract":"<div><p>We describe the ordering of a class of clones by minion homomorphisms, also known as minor preserving maps or height 1 clone homomorphisms. The class consists of all clones on finite sets determined by binary relations whose projections to both coordinates have at most two elements. This class can be alternatively described up to minion homomorphisms as the class of multisorted Boolean clones determined by binary relations. We also introduce and apply the concept of a minion core which provides canonical representatives for equivalence classes of clones, more generally minions, on finite sets.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142595556","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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