Idempotent-Conjugate Monoids with Nilpotent Unit Groups

Let M be a finite monoid with unit group G such that J-related idempotents in M are conjugate. If G is nilpotent, we prove that the complex monoid algebra CM of M is semisimple if and only if M is an inverse monoid. Conversely let G be a finite group such that for any finite idempotent-conjugate monoid M with unit group G, CM semisimple implies that M is an inverse monoid. We then show that G is a nilpotent group.     

On rigid monoids and 2-fir monoid rings

It is proved that the universal group of a torsion free rigid monoid is torsion free. As a consequence, a new condition on a monoid M for the monoid ring R[M] to be a 2-fir is given. Furthermore, the monoids between a rigid monoid and its universal group are studied.     

相对于幺半群的McCoy环的扩张

对于幺半群~$M$, 本文引入了~$M$-McCoy~环.~证明了~$R$~是~$M$-McCoy~环当且仅当~$R$~上的~$n$~阶上三角矩阵环~$aUT_n(R)$~是~$M$-McCoy~环;得到了若~$R$~是~McCoy~环,~$R[x]$~是~$M$-McCoy~环,则~$R[M]$~是~McCoy~环;对于包含无限循环子半群的交换可消幺半群~$M$,证明了若~$R$~是~$M$-McCoy~环,则半群环~$R[M]$~是~McCoy~环及~$R$~上的多项式环~$R[x]$~是~$M$-McCoy~环.     

Presentations of Bruck-Reilly Extensions and Decision Problems

We show that any Bruck-Reilly extension of an inverse monoid is an HNN extension of a certain inverse monoid. We also discuss several decision problems. The word problem for a Bruck-Reilly extension of an inverse monoid is solvable under a reasonable condition. On the other hand, many algebraic properties for Bruck-Reilly extensions of inverse monoids are undecidable. Key words : Inverse monoids, Bruck-Reilly extensions, HNN extensions, Decision problems. AMS Mathematics Subject Classification: 20M18, 20M05     

Representations of Inverse Monoids by Partial Automorphisms

It is shown that any inverse semigroup of endomorphisms of an object in a properly (E, M)-structured category admitting intersections may be embedded in an inverse monoid of partial automorphisms between retracts of that object. It follows that every inverse monoid is isomorphic with an inverse monoid of all partial automorphisms between [non-trival] retracts of some object of any [almost] algebraically universal and properly (E, M)-structured category with intersections; in particular, of an [almost] algebraically universal and finitely complete category with arbitrary intersections. Several examples are given.     

On graphs with a given endomorphism monoid

Hedrlín and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M . In this paper we give a construction G(M) for a graph with prescribed endomorphism monoid M . Using this construction we derive bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. For example we show that for every monoid M , | M |=m there is a graph G with End(G)? M and |E(G)|≤(1 + 0(1))m². This is, up to a factor of 1/2, best possible since there are monoids requiring a graph with \begin{eqnarray*} && \frac{m^{2}}{2}(1 -0(1)) \end{eqnarray*} edges. We state bounds for the class of all monoids as well as for certain subclasses—groups, k‐cancellative monoids, commutative 3‐nilpotent monoids, rectangular groups and completely simple monoids. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 241–262, 2009     

Baer Criterion for Injectivity of Projection Algebras

Projection algebras are M-sets for the monoid M = (ℕ^∞, min) which are used by computer scientists for algebraic specification of process algebras. In contrast to the case of modules it is well known that the Baer Criterion does not generally hold for injectivity of M-sets for an arbitrary monoid M. Here, introducing a closure operator, we prove that the Baer Criterion does hold for injectivity of projection algebras.     

Endomorphism monoids and topological subgraphs of graphs

We prove, that, given a finite graph Y there exists a finite monoid (semigroup with unity) M such that any graph X whose endomorphism monoid is isomorphic to M contains a subdivision of Y. This contrasts with several known results on the simultaneous prescribability of the endomorphism monoid and various graph theoretical properties of a graph. It is also related to the analogous problems on graphs having a given permutation group as a restriction of their automorphism group to an invariant subset.     

Generators and presentations for direct and wreath products of monoid acts

Semigroup Forum - We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid M is said to...     

A Note on the n-Generator Property for Commutative Monoids

Let M be a cancellative, commutative monoid with integral closure . Borrowing from ring theory, we say that M has the n-generator property iff every finitely generated ideal of M can be generated by n elements, and we say M has rank n iff every ideal of M can be generated by n elements. We investigate the integral closure of such monoids. We show, in particular, that if M has the n-generator property, then is a valuation monoid, and if M has rank n, then is a principal ideal monoid.     

M-McCoy环和M-Armendariz环的多项式扩张

研究非交换环上的相对于幺半群的McCoy环和Armendariz环的多项式扩张.对于包含无限循环子幺半群的交换可消幺半群M,证明了若R是M-McCoy（或M-Armendariz）环,则R上的洛朗多项式环R[x,x-1]是M-McCoy（或M-Armendariz）环.     

Right-veering diffeomorphisms of compact surfaces with boundary

We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight contact structures and open book decompositions. Mathematics Subject Classification (1991) Primary 57M50, secondary 53C15     

Numerical semigroups bounded by the translation of a plane monoid

Aequationes mathematicae - Let $$\mathbb {N}$$ be the set of nonnegative integer numbers. A plane monoid is a submonoid of $$(\mathbb {N}^2,+)$$ . Let M be a plane monoid and $$p,q\in \mathbb {N}$$...     

A New Variant of Wilson’s Functional Equation on Monoids

Acta Mathematica Sinica, English Series - We find on a monoid M the complex-valued solutions f, g : M → ? such that f is central and g is continuous of the functional equation $$f\left(...     

A Note on Prehomomorphisms

We show that if G is a free group with basis X then any map θ from X to an inverse monoid S extends to a monoid prehomomorphism ψ: G\rightarrow S. As an application we give an affirmative answer to a problem of M. Petrich. 1980 Mathematics Subject Classification: Primary 20M10. September 14, 1999     

The intersection of free submonoids of a free monoid is free

Several necessary and sufficient conditions exist for a submonoid of a free monoid to be free. For a few, see [1] through [6]. This short note uses one of these conditions, due to Schützenberger (see [2], p. 119, or [4], Theorem 1.4) to establish that the intersection of free submonoids of a free monoid M is again free. Schützenberger's condition is also proven in this note.     

Equipotence et unicite de systemes generateurs minimaux dans certains monoides

It is proved that in a periodic ℛ-trivial monoid M, any two minimal generating systems have the same cardinality. Morever if M isT-trivial and admits a minimal generating system then such a system is unique.      

Interpreting the Action of the Endomorphism Monoid of the Rationals

Algebra and Logic - In a first order language we interpret the action of the monoid M of embeddings of (?,<) on the set ? inside (M,°). A similar result is proved for the...     

广义逆多项式模的co-Hopf性质

设R是结合环(可以没有单位元),(S,≤)是严格全序幺半群,序≤是Artin的且对任意s∈S,有0≤s,则对任意具有性质(F)的左R-模M,[MS,≤]是co-Hopf左[[RS,≤]]一模当且仅当M是co-Hopf左R-模.     

Monoid Properties as Invariants of Toposes of Monoid Actions

Applied Categorical Structures - We systematically investigate, for a monoid M, how topos-theoretic properties of $${{\,\mathrm{\mathbf {PSh}}\,}}(M)$$ , including the properties of being atomic,...