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The Priestley duality for (prec )-distributive (vee )-predomains (prec ) -分布(vee ) -前域的Priestley对偶性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-09-29 DOI: 10.1007/s00012-025-00907-6
Ao Shen, Xiaodong Jia, Hualin Miao, Qingguo Li
{"title":"The Priestley duality for (prec )-distributive (vee )-predomains","authors":"Ao Shen,&nbsp;Xiaodong Jia,&nbsp;Hualin Miao,&nbsp;Qingguo Li","doi":"10.1007/s00012-025-00907-6","DOIUrl":"10.1007/s00012-025-00907-6","url":null,"abstract":"<div><p>In this paper, we present a Priestley-type topological representation for <span>(prec )</span>-distributive <span>(vee )</span>-predomains, thereby answering an open problem posed by T. Bice. Moreover, we establish a dual equivalence between the category of <span>(prec )</span>-distributive <span>(vee )</span>-predomains with <span>(prec )</span>-morphisms and that of DP-compact pospaces with DP-morphisms. In particular, our results restrict to Hansoul-Poussart duality for bounded distributive sup-semilattices and to a Priestley duality for continuous frames.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210301","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 note on the probability of a groupoid having deficient sets 关于群类群有亏集的概率的注释
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-09-22 DOI: 10.1007/s00012-025-00906-7
Carles Cardó
{"title":"A note on the probability of a groupoid having deficient sets","authors":"Carles Cardó","doi":"10.1007/s00012-025-00906-7","DOIUrl":"10.1007/s00012-025-00906-7","url":null,"abstract":"<div><p>A subset <i>X</i> of a groupoid is said to be deficient if <span>(|X cdot X|le |X|)</span>. It is well-known that the probability that a random groupoid has a deficient <i>t</i>-element set with <span>(tge 3)</span> is zero. However, it is believed that the probability is not zero for 2-element sets. We prove that it is indeed not null and calculate the exact value. We explore some generalisations on deficient sets and their likelihoods.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167664","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 prime spectrum of (ell )-groups and MV-algebras (ell ) -群与mv -代数的素谱
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-09-22 DOI: 10.1007/s00012-025-00905-8
Giuseppina G. Barbieri, Antonio di Nola, Giacomo Lenzi
{"title":"The prime spectrum of (ell )-groups and MV-algebras","authors":"Giuseppina G. Barbieri,&nbsp;Antonio di Nola,&nbsp;Giacomo Lenzi","doi":"10.1007/s00012-025-00905-8","DOIUrl":"10.1007/s00012-025-00905-8","url":null,"abstract":"<div><p>As a main result, we characterize prime spectra of abelian lattice ordered groups. Further we introduce some categories based on spectral spaces, lattices and Priestley spaces. Then we have a characterization of the variety generated by the Chang MV-algebra and we study this variety. Next we generalize the results to every variety generated by a Komori chain.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00905-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110616","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
Boolean rigs 布尔钻井平台
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-09-12 DOI: 10.1007/s00012-025-00904-9
Daniel Misselbeck-Wessel, Iosif Petrakis
{"title":"Boolean rigs","authors":"Daniel Misselbeck-Wessel,&nbsp;Iosif Petrakis","doi":"10.1007/s00012-025-00904-9","DOIUrl":"10.1007/s00012-025-00904-9","url":null,"abstract":"<div><p>Semirings of partial Boolean-valued functions arise in Bishop’s approach to constructive measure theory. In this paper, we treat such semirings axiomatically. Lifting the corresponding result for Boolean rings, we prove a representation theorem à la Stone that aligns with the intended semantics. Moreover, among the semirings at hand, we determine the order of those that are free over finitely many generators.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037355","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 core quandles 在核心quandles
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-08-30 DOI: 10.1007/s00012-025-00901-y
Filippo Spaggiari, Marco Bonatto
{"title":"On core quandles","authors":"Filippo Spaggiari,&nbsp;Marco Bonatto","doi":"10.1007/s00012-025-00901-y","DOIUrl":"10.1007/s00012-025-00901-y","url":null,"abstract":"<div><p>We characterize several properties of core quandles in terms of the properties of their underlying groups. Specifically, we characterize connected cores providing an answer to an open question and present a standard homogeneous representation for them, which allows us to prove that simple core quandles are primitive.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920495","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
Free strict n-tuple semigroups are determined by their endomorphism semigroups 自由严格n元半群由它们的自同态半群决定
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-08-30 DOI: 10.1007/s00012-025-00903-w
Anatolii V. Zhuchok
{"title":"Free strict n-tuple semigroups are determined by their endomorphism semigroups","authors":"Anatolii V. Zhuchok","doi":"10.1007/s00012-025-00903-w","DOIUrl":"10.1007/s00012-025-00903-w","url":null,"abstract":"<div><p>The problem of determinability for free algebras in a given variety was posed by B. I. Plotkin in his lectures on universal algebraic geometry. This problem has been solved for free groups by E. Formanek, and for free semigroups and free monoids by G. Mashevitsky and B. M. Schein. We solve the determinability problem for free strict <i>n</i>-tuple semigroups as a natural generalization of free semigroups.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920494","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
Słupecki digraphs
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-08-26 DOI: 10.1007/s00012-025-00900-z
Ádám Kunos, Benoît Larose, David Emmanuel Pazmiño Pullas
{"title":"Słupecki digraphs","authors":"Ádám Kunos,&nbsp;Benoît Larose,&nbsp;David Emmanuel Pazmiño Pullas","doi":"10.1007/s00012-025-00900-z","DOIUrl":"10.1007/s00012-025-00900-z","url":null,"abstract":"<div><p>Call a finite relational structure <i>k-Słupecki</i> if its only surjective <i>k</i>-ary polymorphisms are essentially unary, and <i>Słupecki</i> if it is <i>k</i>-Słupecki for all <span>(k ge 2)</span>. We present conditions, some necessary and some sufficient, for a reflexive digraph to be Słupecki. We prove that all digraphs that triangulate a 1-sphere are Słupecki, as are all the ordinal sums <span>(m oplus n)</span> (<span>(m,n ge 2)</span>). We prove that the posets <span>(mathbb {P}= m oplus n oplus k)</span> are not 3-Słupecki for <span>(m,n,k ge 2)</span>, and prove there is a bound <i>B</i>(<i>m</i>, <i>k</i>) such that <span>(mathbb {P})</span> is 2-Słupecki if and only if <span>(n &gt; B(m,k)+1)</span>; in particular there exist posets that are 2-Słupecki but not 3-Słupecki.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00900-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144905214","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
A choice-free proof of Mal’cev’s theorem on quasivarieties 马尔切夫定理在拟变量上的无选择证明
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-08-21 DOI: 10.1007/s00012-025-00902-x
Guozhen Shen
{"title":"A choice-free proof of Mal’cev’s theorem on quasivarieties","authors":"Guozhen Shen","doi":"10.1007/s00012-025-00902-x","DOIUrl":"10.1007/s00012-025-00902-x","url":null,"abstract":"<div><p>In 1966, Mal’cev proved that a class <span>(mathcal {K})</span> of first-order structures with a specified signature is a quasivariety if and only if <span>(mathcal {K})</span> contains a unit and is closed under isomorphic images, substructures, and reduced products. In this article, we present a proof of this theorem in <span>(textsf{ZF})</span> (i.e., the Zermelo–Fraenkel set theory without the axiom of choice).</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887972","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
Partial commutators 部分换向片
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-06-30 DOI: 10.1007/s00012-025-00899-3
Vaino T. Shaumbwa
{"title":"Partial commutators","authors":"Vaino T. Shaumbwa","doi":"10.1007/s00012-025-00899-3","DOIUrl":"10.1007/s00012-025-00899-3","url":null,"abstract":"<div><p>We introduce a notion of <i>partial commutator</i> in the context of a normal category with cokernels, as the commutator resulting from the recently introduced notion of <i>partial commutativity</i>. The partial commutator is defined by making slight modifications to the definition of the Huq commutator, and they agree in the unital context. We show that some fundamental properties of the Huq commutator can still be recovered. In particular, the partial commutator vanishes if and only if the morphisms partially commute, and in a normal category with finite colimits, it always exists and can be obtained via colimits as it is the case in absolute settings. As an application, we investigate partial commutators in the category <span>(textsf{LAlg})</span> of <i>L</i>-algebras in the sense of W. Rump.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145262","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 maximal ring of quotients of (A_d L) 的商的极大环 (A_d L)
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-06-23 DOI: 10.1007/s00012-025-00895-7
Warren Wm. McGovern, Batsile Tlharesakgosi
{"title":"The maximal ring of quotients of (A_d L)","authors":"Warren Wm. McGovern,&nbsp;Batsile Tlharesakgosi","doi":"10.1007/s00012-025-00895-7","DOIUrl":"10.1007/s00012-025-00895-7","url":null,"abstract":"<div><p>We start with a zero-dimensional frame <i>L</i> and an arbitrary integral domain <i>A</i>. We equip <i>A</i> with the discrete topology and consider the ring of <i>A</i>-valued continuous functions on <i>L</i>, which we denote by <span>(A_dL)</span>. In this article, we classify both the classical ring of quotients and maximal ring of quotients of <span>(A_dL)</span>, paying special attention to the case of <span>({mathfrak Z}L)</span> the integer-valued continuous functions on <i>L</i>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144560","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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