Related papers: On idempotent generated semigroups
We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.
We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup $S$. By nonstandard and topological arguments, we show Ramsey…
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
We show that every finitely generated residually finite torsion group $G$ embeds in a finitely generated torsion group $\Gamma$ that is residually finite simple. In particular we show the existence of finitely generated infinite torsion…
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathematics can be treated as a result of a dequantization of the…
We prove that every non-abelian finite simple group is generated by an involution and an element of prime order.
In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to…
The second author introduced notions of weak permutability and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite groups. Two groups H,K weakly commute provided there exists a…
Hindman and Leader first introduced the notion of semigroup of ultrafilters converging to zero for a dense subsemigroups of $((0,\infty),+)$. Using the algebraic structure of the Stone-$\breve{C}$ech compactification, Tootkabani and Vahed…
A smallest generating set of a semigroup is a generating set of the smallest cardinality. Similarly, an irredundant generating set $X$ is a generating set such that no proper subset of $X$ is also a generating set. A semigroup $S$ is…
We gave an alternative short proof on the finite generation of holomorphic functions with polynomial growth on Riemann surfaces with nonnegative curvature. The first proof was due to Li and Tam.
We give a short proof of an idempotent relation formula for counting periodic points of endomorphisms defined over finite fields. The original proof of this result, due to Walton, uses formal manipulation of arithmetic zeta functions,…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
We offer in this note a self-contained proof of the fact that a finitely generated group is not virtually nilpotent if and only if it has a quotient with the infinite conjugacy class (ICC) propoerty. This proof is a modern presentation of…
We prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization as quasi-geodesic monoids, and show that their word problem is rational (as a…
Some results that are true in classical groups are investigated in generalized groups and are shown to be either generally true in generalized groups or true in some special types of generalized groups. Also, it is shown that a Bol groupoid…
In this paper, we introduce a method computing the primitive decomposition of idempotents of any semisimple finite group algebra based on its matrix representations and Wedderburn decomposition. Particularly, we use this method to calculate…
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdirectly irreducible members of the variety of semilinear…
Let $V$ be a quasiprojective variety defined over $\mathbb{F}_q$, and let $\phi:V\rightarrow V$ be an endomorphism of $V$ that is also defined over $\mathbb{F}_q$. Let $G$ be a finite subgroup of $\operatorname{Aut}_{\mathbb{F}_q}(V)$ with…