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About 4,321 papers for “Monoid”

Monoid Properties as Invariants of Toposes of Monoid Actions

Jens Hemelaer, Morgan Rogers · Applied Categorical Structures · 2020

Abstract We systematically investigate, for a monoid M , how topos-theoretic properties of $${{\,\mathrm{\mathbf {PSh}}\,}}(M)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mspace/><mml:mi>PSh</mml:mi><mml:mspace/></mml:mrow><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> , including the properties of being atomic, strongly compact, local, totally connected or cohesive, correspond to semigroup-theoretic properties of M .

Cited by 1Open access

The Chinese monoid

Cassaigne, J., Espie, M., Krob, D. et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2001

International audience

Cited by 0

On monoid graphs

Kolja Knauer, Gil Puig I Surroca · arXiv (Cornell University) · 2021

We investigate Cayley graphs of finite semigroups and monoids. First, we look\nat semigroup digraphs, i.e., directed Cayley graphs of semigroups, and give a\nSabidussi-type characterization in the case of monoids. We then correct a proof\nof Zelinka from '81 that characterizes semigroup digraphs with outdegree $1$.\nFurther, answering a question of Knauer and Knauer, we construct for every\n$k\\geq 2$ connected $k$-outregular non-semigroup digraphs. On the other hand,\nwe show that every sink-free directed graph is a union of connected components\nof a monoid digraph.\n Second, we consider monoid graphs, i.e., underlying simple undirected graphs\nof Cayley graphs of monoids. We show that forests and threshold graphs form\npart of this family. Conversely, we construct the -- to our knowledge -- first\ngraphs, that are not monoid graphs. We present non-monoid graphs that are\nplanar, have arboricity $2$, and treewidth $3$ on the one hand, and non-monoid\ngraphs of arbitrarily high connectivity on the other hand.\n Third, we study generated monoid trees, i.e., trees that are monoid graphs\nwith respect to a generating set. We give necessary and sufficient conditions\nfor a tree to be in this family, allowing us to find large classes of trees\ninside and outside the family.\n

Cited by 0Open access

The stylic monoid

Antoine Abram, Christophe Reutenauer · Semigroup Forum · 2022

Cited by 12

The chinese monoid

Cassaigne, Julien, Espie, Marc, Hivert, Florent et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2001

Nous étudions les propriétés combinatoires du monoïde chinois.

Cited by 0Open access

SEMIHEREDITARY MONOID RINGS

James Kuzmanovich, Mark L. Teply, James Kuzmanovich et al. · 2015

Hereditary and semihereditary rings have been the subject of considerable study. Many interesting examples of these rings arise as group rings or semigroup rings. Recently Chouinard, Hardy, and Shores [3] have completely determined the commutative semihereditary monoid rings. Goursaud and Valette [8] have given results concerning hereditary and semihereditary group rings, while Dicks [5] has completely determined the hereditary group rings. In this paper we continue the study of semihereditary monoid rings. Let R be a not necessarily commutative ring with identity, and let S be a monoid. We characterize in terms of R and S the left semihereditary monoid rings R[S] when S is a semilattice of torsion groups. This yields a characterization of the left semihereditary monoid rings R[S] when S is commutative and periodic. If S is a non-periodic commutative monoid, we show that a necessary condition for R[S] to be left semihereditary is that Z(R)[S] be semihereditary and R be yon Neumann regular. In view of results of [3], this yields much information about the structure of S. If, in addition, S is a strong semilattice of commutative groups, then necessary and sufficient conditions for R[S] to be left semihereditary are obtained. Our main tool is a technical lemma (Lemma 3), which may have independent interest in determining whether or not a ring is semihereditary. Throughout this paper all rings will be associative with identity. We will use Z(R) to denote the center of a ring R, and œR(X) to denote the left annihilator in R of an element x. The ring of n X n matrices over R will be denoted by Mn(R). A semilattice Y is a commutative semigroup all of whose elements are idempotent; such a Y has a natural ordering denoted by •&amp;lt;. In [10], [17] and other papers, a ring R is called a supplementary semilattice sum of rings R a (a C Y) if the following conditions hold: R = Zo•cyRo•, Ro•R$3 _C Ro•s3 for all o•,S3 • Y, and Ro • C•

Cited by 0

The Plactic Monoid

Lascoux, Alain, Leclerc, B., Thibon, Jean-Yves · HAL (Le Centre pour la Communication Scientifique Directe) · 2002

incollection

Cited by 0

Semigrup Dan Monoid

Zulfarisna · Andalas University Repository (Andalas University) · 2008

Cited by 0

THE CHINESE MONOID

Julien Cassaigne, Espie Marc, Daniel Krob et al. · International Journal of Algebra and Computation · 2001

Résumé: Cet article présente une étude combinatoire du monoïde Chinois, un monoïde ternaire proche du monoïde plaxique, fondé sur le schéma cba≡bca≡cab. Un algorithme proche de l'algorithme de Schensted nous permet de caractériser les classes d'équivalence et d'exhiber une section du monoïde. Nous énonçons également une correspondance de Robinson–Schensted pour le monoïde Chinois avant de nous intéresser au calcul du cardinal de certaines classes. Ce travail a permis de développer de nouveaux outils combinatoires. Entre autres, nous avons trouvé un plongement de chacune des classes d'équivalence dans la plus grande classe. Quant à la dernière partie de cet article, elle présente l'étude des relations de conjugaison. This paper presents a combinatorial study of the Chinese monoid, a ternary monoid related to the plactic monoid and based on the relation scheme cba≡bca≡cab. An algorithm similar to Schensted's algorithm yields a characterization of the equivalence classes and a cross-section theorem. We also establish a Robinson–Schensted correspondence for the Chinese monoid before computing the order of specific Chinese classes. For this work, we had to develop some new combinatorial tools. Among other things we discovered an embedding of every equivalence class in the largest one. Finally, the end of this paper is devoted to the study of conjugacy classes.

Cited by 39

The Geometry Monoid

Patrick Dehornoy · Birkhäuser Basel eBooks · 2000

Studying free LD-systems amounts to studying LD-equivalence of terms. Now t= LD t’ holds ift can be transformed into t’ by iteratively applying the left self-distributivity identity, which can be seen as applying some operator that specifies where and how (from left to right or from right to left) the identity is applied. Applying the identity several times amounts to composing the associated operators. So we obtain a monoid of (partial) operators acting on terms, so that the LD-equivalence class of a term is its orbit under the action. The aim of this chapter is to study the monoid GLDinvolved in this action, which we call the geometry monoid of(LD)as it captures a number of geometrical relations involving left self-distributivity.

Cited by 0

The Chinese Monoid

Julien Cassaigne, Marc Espie, Florent Hivert et al. · 2007

This paper presents a combinatorial study of the Chinese monoid, a ternary monoid related to the plactic monoid and based on the rewritings cba j bca j cab.

Cited by 0

The Chinese Monoid

Julien Cassaigne, Marc Espie, Florent Hivert et al. · 2007

This paper presents a combinatorial study of the Chinese monoid, a ternary monoid related to the plactic monoid and based on the rewritings cba j bca j cab. An algorithm similar to Schensted&amp;apos;s algorithm yields a characterisation of the equivalence classes and a cross-section theorem. We also establish a RobinsonSchensted correspondence for the Chinese monoid before computing the order of specific Chinese classes. For this work, we had to develop some new combinatorial tools. Among other things we discovered an embedding of every equivalence class in the greatest one. Finally, the end of this paper is devoted to the study of conjugacy classes.

Cited by 0