Annihilator Properties of Skew Monoid Rings

Let R be a ring with an endomorphism σ and F ∪ {0} the free monoid generated by U = {u ₁,…, u _t } with 0 added, and M a factor of F setting certain monomial in U to 0, enough so that, for some n, M ⁿ  = 0. In this article, we study various annihilator properties and a variety of conditions and related properties that the skew monoid ring R[M; σ] is inherited from R.     

On Semihereditary and p.p. Monoid Rings

No Abstract. June 30, 1998     

Relative Regular Modules. Applications to von Neumann Regular Rings

We use the concept of a regular object with respect to another object in an arbitrary category, in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R −mod and S −mod, when S is an excellent extension of the ring R. Consequently, if S is an excellent extension of the ring R, then S is von Neumann regular ring if and only if R is also von Neumann regular ring. In the second part, using relative regular modules, we give a new proof of a classical result: the von Neumann regular property of a ring is Morita invariant.     

The Center of a Regular Algebraic Monoid

This paper is devoted to proving the following result: Let M be an irreducible regular algebraic monoid with unit group G. Then the center of M is unit regular and coincides with the closure of the center of G. Moreover if the M is reductive, then its center also coincides with the intersection of all maximal diagonizable submonoids of M.     

幺半群上的广义内射S-系(英文)

本文考虑拟内射、伪内射、核内射以及支内射S-系的性质,重点讨论这些广义内射S-系的上的线性方程组的性质.例如,A是核内射S-系当且仅当A的任意收缩核B上的任意A-相容线性方程组在B上是可解的;A是支内射S-系当且仅当同构于A的任一分支的S-系B上的任意A-相容线性方程组在B上是可解的.进而讨论了伪内射、核内射以及支内射S-系的融合余积的性质.最后给出了一个充分条件,基于此条件核内射和支内射S-系是等价的.     

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,...     

Band Monoid Languages Revisited

We describe the atoms of the varieties of band monoid languages as disjoint unions of concatenations of words and free monoids. We present a new proof of a solution of the word problem for the free band due to Siekman and Szabo.     

A Polynomial Time Algorithm to Compute the Abelian Kernel of a Finite Monoid

Abstract. The time complexity of the best previously known algorithm to compute the Abelian kernel of a finite monoid with a fixed number of generators is exponential. In this paper we use results on subgroups of the free Abelian group and constructions on labeled graphs to develop a polynomial time algorithm for this problem.     

图半群的结构

该文在图(的自同态)半群中引入了拟格林关系概念;给出了拟格林关系的性质;然后在此基础上进一步证明了图半群的(格林关系意义上的)双重结构性质     

Relative Completions and the Cohomology of Linear Groups Over Local Rings

For a discrete group G there are two well known completions.The first is the Malcev (or unipotent) completion. This is aprounipotent group U, defined over Q, together with a homomorphism : G U that is universal among maps from G into prounipotentQ-groups. To construct U, it suffices for us to consider thecase where G is nilpotent; the general case is handled by takingthe inverse limit of the Malcev completions of the G/^rG, where^•G denotes the lower central series of G. If G is abelian,then U = G Q. We review this construction in Section 2.     

Constructions of Partial Difference Sets and Relative DifferenceSets Using Galois Rings

We use Galois rings to construct partial difference sets and relative difference sets in non-elementary abelianp-groups. As an example, we also use Galois ringG R(4, 2) to construct a (96,20,4) difference set in Z₄ × Z₄ × Z₆.Dedicated to Hanfried Lenz on the occasion of his 80th birthday     

Generalized Affine Transformation Monoid of a Residue Class Ring

In this paper, we consider the generalized affine transformation monoid Gaff (A/I) of a residue class ring A/I of a commutative ring A with identity modulo its nonzero ideal I. For the general case, we investigate the Green's relations, Schutzenberger group for every D-class and, the structure of group H-classes, regular D-classes, the idempotent set E(Gaff (A/I)) and the regular element set Reg (Gaff (A/I)) of Gaff (A/I). If A is an integral domain and I a product of powers of invertible maximal ideals, we show that Gaff (A/I) is an epigroup, every R^⋆-classes of Gaff (A/I) is a nil-extension of a right group and that Gaff (A/I) is a complete lattice of nil-extensions of right groups.     

Monoid extensions admitting cocycles

We characterize those monoid extensions which are associated to a certain class of 2 -cocycles. Algebraic, topological as well as involutive aspects are discussed. Applications to representation theory are given.     

Idempotent Generation in the Endomorphism Monoid of a Uniform Partition

Denote by 𝒯_n and 𝒮_n the full transformation semigroup and the symmetric group on the set {1,…, n}, and ?_n = {1} ∪ (𝒯_n?𝒮_n). Let 𝒯(X, 𝒫) denote the monoid of all transformations of the finite set X preserving a uniform partition 𝒫 of X into m subsets of size n, where m, n ≥ 2. We enumerate the idempotents of 𝒯(X, 𝒫), and describe the submonoid S = ? E ? generated by the idempotents E = E(𝒯(X, 𝒫)). We show that S = S₁ ∪ S₂, where S₁ is a direct product of m copies of ?_n, and S₂ is a wreath product of 𝒯_n with 𝒯_m?𝒮_m. We calculate the rank and idempotent rank of S, showing that these are equal, and we also classify and enumerate all the idempotent generating sets of minimal size. In doing so, we also obtain new results about arbitrary idempotent generating sets of ?_n.