Rees matrix seminearring

As a continuation of the work done in (R. Mukherjee (Pal), P. Pal and S. K. Sardar, On additively completely regular seminearrings, Commun. Algebra 45(12) (2017) 5111–5122), in this paper, our objective is to characterize left (right) completely simple seminearrings in terms of Rees Construction by generalizing the concept of Rees matrix semigroup (J. M. Howie, Fundamentals of Semigroup Theory (Clarendon Press, Oxford, 1995); M. Petrich and N. R. Reilly, Completely Regular Semigroups (Wiley, New York, 1999)) and that of Rees matrix semiring (M. K. Sen, S. K. Maity and H. J. Weinert, Completely simple semirings, Bull. Calcutta Math. Soc. 97 (2005) 163–172). In Rees theorem, a completely simple semigroup is coordinatized in such a way that each element can be seen to be a triplet which gives this abstract structure a much more simpler look. In this paper, we have been able to construct a similar kind of coordinate structure of a restricted class of left (right) completely simple seminearrings taking impetus from (M. P. Grillet, Semirings with a completely simple additive semigroup, J. Austral. Math. Soc. 20(Ser. A) (1975) 257–267, Theorem [Formula: see text] and (M. K. Sen, S. K. Maity and H. J. Weinert, Completely simple semirings, Bull. Calcutta Math. Soc. 97 (2005) 163–172, Theorem [Formula: see text]).

SEMIGRUP REGULER DAN SIFAT-SIFATNYA

This article discusses some properties of regular semigroups. These properties are especially concerned with the relation of the regular semigroups to ideals, subsemigroups, groups, idempoten semigroups and invers semigroups. In addition, this paper also discusses the Cartesian product of two regular semigroups. Keywords:ideal, idempoten semigroup, inverse semigroup, regular semigroup, subsemigroup.

Semigroups whose right ideals are finitely generated

We call a semigroup $S$ weakly right noetherian if every right ideal of $S$ is finitely generated; equivalently, $S$ satisfies the ascending chain condition on right ideals. We provide an equivalent formulation of the property of being weakly right noetherian in terms of principal right ideals, and we also characterize weakly right noetherian monoids in terms of their acts. We investigate the behaviour of the property of being weakly right noetherian under quotients, subsemigroups and various semigroup-theoretic constructions. In particular, we find necessary and sufficient conditions for the direct product of two semigroups to be weakly right noetherian. We characterize weakly right noetherian regular semigroups in terms of their idempotents. We also find necessary and sufficient conditions for a strong semilattice of completely simple semigroups to be weakly right noetherian. Finally, we prove that a commutative semigroup $S$ with finitely many archimedean components is weakly (right) noetherian if and only if $S/\mathcal {H}$ is finitely generated.

Regular and Intra-Regular Semigroups in Terms of m-Polar Fuzzy Environment

The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m-PFSs. This paper provides some important results related to m-polar fuzzy subsemigroups (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs), m-polar fuzzy quasi-ideals (m-PFQIs) and m-polar fuzzy interior ideals (m-PFIIs) in semigroups. This research paper shows that every m-PFBI of semigroups is the m-PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semigroups by the properties of m-PFIs and m-PFBIs.

(m, n)-Ideals in Semigoups Based on Int-Soft Sets

Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. In this paper, we introduce the notions of int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals of semigroups by generalizing the concept of int-soft bi-ideals, int-soft right ideals, and int-soft left ideals in semigroups. In addition, some of the properties of int-soft m , n -ideal, int-soft m , 0 -ideal, and int-soft 0 , n -ideal are studied. Also, characterizations of various types of semigroups such as m , n -regular semigroups, m , 0 -regular semigroups, and 0 , n -regular semigroups in terms of their int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals are provided.

Higher Braid Groups and Regular Semigroups from Polyadic-Binary Correspondence

In this note, we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order) reproduces the regular semigroups and braid groups with their binary multiplication of components. We then generalize the construction to the higher arity case, which allows us to obtain some higher degree versions (in our sense) of the regular semigroups and braid groups. The latter are connected with the generalized polyadic braid equation and R-matrix introduced by the author, which differ from any version of the well-known tetrahedron equation and higher-dimensional analogs of the Yang-Baxter equation, n-simplex equations. The higher degree (in our sense) Coxeter group and symmetry groups are then defined, and it is shown that these are connected only in the non-higher case.