Semigroup Forum最新文献_第7页

Broken Möbius categories of $$Q_{3}$$ -type and their split inverse semigroups Q{3}$ 类的破碎莫比乌斯范畴及其分裂逆半群

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-02-07 DOI: 10.1007/s00233-024-10410-4

Emil Daniel Schwab

{"title":"Broken Möbius categories of $$Q_{3}$$ -type and their split inverse semigroups","authors":"Emil Daniel Schwab","doi":"10.1007/s00233-024-10410-4","DOIUrl":"https://doi.org/10.1007/s00233-024-10410-4","url":null,"abstract":"A class of Möbius monoids leads us to Möbius categories of (Q_{3})-type via a particular breaking process, where (Q_{3}) is a quiver with three arrows (atoms). In this paper we show that a quasi-commutativity regarding composable atoms uniquely determines (via a certain local congruence) a half-factorial broken Möbius category of (Q_{3})-type as a quotient category of the path category of (Q_{3}). Some examples shed light on the development of the topic under discussion. On the other hand, the Möbius breaking process can be extended for inverse semigroups as well. The Leech inverse semigroups of the two broken Möbius categories (the path category of (Q_{3}) and its quotient category) are split inverse semigroups in the sense that both are unions of two proper inverse subsemigroups, that is, both are with covering numbers 2. The connections on the two planes (broken Möbius categories and split inverse semigroups) are made on one hand by a local congruence (varrho ^{+}) of the path category of (Q_{3}), and on the other hand by a normal inverse subsemigroup (G^{+}) namely a gauge inverse subsemigroup. This gauge inverse semigroup is a full inverse subsemigroup of the almost Cartesian product (Btimes _{0}B_{{mathbb {N}}}) of the bicyciclic semigroup B and the Brandt semigroup (B_{{mathbb {N}}}). Special properties of this almost Cartesian product are examined by comparison with the well known polycyclic monoid.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Orderability of the prefix expansion of an ordered inverse semigroup 有序逆半群前缀展开的有序性

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-02-02 DOI: 10.1007/s00233-024-10409-x

G. H. Esslamzadeh, M. A. Faraji, B. Tabatabaie Shourijeh

引用次数: 0

Semigroup collaborations between elementary operations 基本运算之间的半群协作

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-02-02 DOI: 10.1007/s00233-024-10408-y

Sergio R. López-Permouth, Aaron Nicely, Majed Zailaee

{"title":"Semigroup collaborations between elementary operations","authors":"Sergio R. López-Permouth, Aaron Nicely, Majed Zailaee","doi":"10.1007/s00233-024-10408-y","DOIUrl":"https://doi.org/10.1007/s00233-024-10408-y","url":null,"abstract":"Given two operations (*) and (circ ) on a set S, an operation (star ) on S is said to be a collaboration between (*) and (circ ) if for all (a,b in S), (a star b) (in {a *b, acirc b }). Another term for collaborations is two-option operations. We are interested in learning what associative collaborations of two given operations (*) and (circ ) there may be. We do not require that (*) and (circ ) themselves be associative. For this project, as an initial experiment, we consider Plus-Minus operations (i.e. collaborations between addition and subtraction on an abelian group) and Plus-Times operations (i.e. collaborations between the addition and multiplication operations on a semiring.) Our study of Plus-Minus operations focuses on the additive integers but extends to ordered groups. For Plus Times operations, we make some headway in the case of the semiring of natural numbers. We produce an exhaustive list of associative collaborations between the usual addition and multiplication on the natural numbers ({mathbb {N}}). The Plus-Times operations we found are all examples of a type of construction which we define here and that we call augmentations by multidentities. An augmentation by multidentities combines two separate magmas A and B to create another, A(B), having (A sqcup B) as underlying set, and in such a way that the elements of B act as identities over those of A. Hence, B consists of a sort of multiple identities (explaining the moniker multidentities.) When A and B are both semigroups then so is A(B). Understanding the connection between certain collaborations and augmentation by multidenties removes, in several cases, the need for cumbersome computations to verify associativity. A final section discusses connections between group collaborations and skew braces.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139665242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Frobenius problem over number fields with a real embedding 有实数嵌入的数域上的弗罗贝尼斯问题

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-01-29 DOI: 10.1007/s00233-023-10403-9

Alex Feiner, Zion Hefty

引用次数: 0

Affine semigroups of maximal projective dimension-II 最大投影维数-II 的亲和半群

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-01-24 DOI: 10.1007/s00233-023-10405-7

Om Prakash Bhardwaj, Indranath Sengupta

引用次数: 0

Completions of posemigroups by cuts and beyond 通过切分及其他方式补全正名群