On finitely related semigroups

Arabian Journal of Mathematics, 2020

For arbitrary monoids A and B, in Cevik et al. (Hacet J Math Stat 2019:1–11, 2019), it has been recently defined an extended version of the general product under the name of a higher version of Zappa products for monoids (or generalized general product) $$A^{\oplus B}$$ A ⊕ B $$_{\delta }\bowtie _{\psi }B^{\oplus A}$$ δ ⋈ ψ B ⊕ A and has been introduced an implicit presentation as well as some theories in terms of finite and infinite cases for this product. The goals of this paper are to present some algebraic structures such as regularity, inverse property, Green’s relations over this new generalization, and to investigate some other properties and the product obtained by a left restriction semigroup and a semilattice.

Archive for history of exact sciences, 2009

In the history of mathematics, the algebraic theory of semigroups is a relative new-comer, with the theory proper developing only in the second half of the twentieth century. Before this, however, much groundwork was laid by researchers arriving at the study of semigroups from the directions of both group and ring theory. In this paper, we will trace some major strands in the early development of the algebraic theory of semigroups. We will begin with the aspects of the theory which were directly inspired by, and were analogous to, existing results for both groups and rings, before moving on to consider the first independent theorems on semigroups: theorems with no group or ring analogues.

Algebra Universalis, 1988

2015

This paper concerned with basic concepts and some results on (idempotent) semigroup satisfying the identities of three variables. The motivation of taking three for the number of variables has come from the fact that many important identities on idempotent semigroups are written by three or fewer independent variables. We consider the semigroup satisfying the property abc = ac and prove that it is left semi-normal and right quasi-normal. Again an idempotent semigroup with an identity aba = ab and aba = ba (ab = a, ab = b) is always a semilattices and normal. An idempotent semigroup is normal if and only if it is both left quasi-normal and right quasi-normal. If a semigroup is rectangular then it is left and right semi-regular.

Arxiv preprint arXiv: …, 2010

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

Bulletin of the American Mathematical Society, 1970

Semigroup theory is a thriving field in modern abstract algebra, though perhaps not a very well-known one. In this article, we give a brief introduction to the theory of algebraic semigroups and hopefully demonstrate that it has a flavor quite different from that of group theory. In the first few sections, we build up some basic semigroup theory, always with the group analogy at the back of our minds. Then, once we have established enough theory, we break free of this restriction and see some truly “independent” semigroup theory. In the final section, we consider the application of semigroups to the study of “partial symmetries.”

Journal of Algebra, 1998

Pacific Journal of Mathematics, 1970

Advances in Mathematics, 1973