Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: If any product of three elements of an inverse semigroup S can be reordered, then S is solvable; the same is not true for any integer number greater than three as discussed by the authors.
Abstract: If any product of three elements of an inverse semigroup S can be re-ordered, then S is solvable; the same is not true for any integer number greater than three.
1 citations
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TL;DR: D'Aquino and Macintyre as discussed by the authors gave axioms for a class of ordered structures, called truncated ordered abelian groups (TOAGs) carrying an addition.
Abstract: We give axioms for a class of ordered structures, called truncated ordered abelian groups (TOAG’s) carrying an addition. TOAG’s come naturally from ordered abelian groups with a 0 and a $$+$$
, but the addition of a TOAG is not necessarily even a cancellative semigroup. The main examples are initial segments $$[0, \tau ]$$
of an ordered abelian group, with a truncation of the addition. We prove that any model of these axioms (i.e. a truncated ordered abelian group) is an initial segment of an ordered abelian group. We define Presburger TOAG’s, and give a criterion for a TOAG to be a Presburger TOAG, and for two Presburger TOAG’s to be elementarily equivalent, proving analogues of classical results on Presburger arithmetic. Their main interest for us comes from the model theory of certain local rings which are quotients of valuation rings valued in a truncation [0, a] of the ordered group $${\mathbb {Z}}$$
or more general ordered abelian groups, via a study of these truncations without reference to the ambient ordered abelian group. The results are used essentially in a forthcoming paper (D’Aquino and Macintyre, The model theory of residue rings of models of Peano Arithmetic: The prime power case, 2021, arXiv:2102.00295
) in the solution of a problem of Zilber about the logical complexity of quotient rings, by principal ideals, of nonstandard models of Peano arithmetic.
1 citations
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TL;DR: In this article, the inverse semigroup associated to the Cuntz-Li relations is shown to be strongly 0-E unitary and is an F∗-inverse semigroup.
Abstract: In this article, we prove that the inverse semigroup associated to the Cuntz-Li relations is strongly 0-E unitary and is an F∗-inverse semigroup. We also identify the universal group of the inverse semigroup. This gives a conceptual explanation for the result obtained in S. Sundar (arXiv:1201.4620v1, 2012).
1 citations
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09 Apr 2012
TL;DR: The structure of the semigroup of all endomorphisms of an endomapping of a finite set has been determined by GANIT as mentioned in this paper, where the endomorphism is represented by a directed graph.
Abstract: The structure of the semigroup of all endomorphisms of an endomapping of a finite set has been determined. This has been done by naturally representing the endomapping by a directed graph, and determining the structure of the endomorphism semigroup of this graph. DOI: http://dx.doi.org/10.3329/ganit.v31i0.10310 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 71-77
1 citations