Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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TL;DR: In this paper, a simple solution of the word problem in the free combinatorial strict inverse semigroup is presented, where the associated partial order is realized as a set of symmetric and transitive relations on a certain set and the corresponding Brandt semigroups as well as the partial homomorphisms can be obtained in a canonical way.
9 citations
TL;DR: In this article, the authors investigate the r-ideal semigroup of a monoid and an ideal system on it, and provide conditions on the monoid such that the idempotents of the ideal system are trivial or π∗-stable.
Abstract: Let H be a monoid (resp. an integral domain) and r an ideal system on H. In this paper we investigate the r-ideal semigroup of H. One goal is to specify monoids such that their r-ideal semigroup possesses semigroup-theoretical properties, like almost completeness, π-regularity and completeness. Moreover if H is an integral domain and ∗ a star operation on H, then we provide conditions on H such that the idempotents of the ∗-ideal semigroup are trivial or such that H is π∗-stable.
9 citations
TL;DR: In this paper, the authors introduce the notion of spectral analysis on the rook monoid and characterize its output in terms of symmetric group spectral analysis, and provide an application to the statistical analysis of partially ranked (voting) data.
Abstract: Motivated by the notion of symmetric group spectral analysis developed by Diaconis, we introduce the notion of spectral analysis on the rook monoid (also called the symmetric inverse semigroup), characterize its output in terms of symmetric group spectral analysis, and provide an application to the statistical analysis of partially ranked (voting) data. We also discuss generalizations to arbitrary finite inverse semigroups. This paper marks the first non-group semigroup development of spectral analysis.
9 citations
01 Feb 1981
TL;DR: In this article, the syntactic monoid syn(H) is characterized as a monoid with a disjunctive,A-zero, and the two particular interesting cases when synH is a nil monoid and when syn H is a semillatice are also characterized.
Abstract: If X* is the free monoid generated by the alphabet X, then any subset L of X* is called a language over X. If PL is the principal congruence determined by L, then the quotient monoid syn(L) = X*/PL is called the syntactic monoid of L. A hypercode over X is any set of nonemtpy words that are noncomparable with respect to the embedding order of X*. If H is a hypercode, then the language H = {xlx E X* and a < x for some a E H) is a right convex ideal of X*. The syntactic monoid syn(H) can be characterized as a monoid with a disjunctive ,A-zero. The two particular interesting cases when syn(H) is a nil monoid and when syn(H) is a semillatice are also characterized.
9 citations
9 citations