Rajlaxmi Mukherjee (Pal)

Garhbeta College · Department of Mathematics

The Action graph of a semigroup act was defined by the authors in [P. Mukherjee, R. Mukherjee and S. K. Sardar, Action graph of a semigroup act [Formula: see text] its functorial connection, Categ. Gen. Algebr. Struct. Appl. 18(1) (2023) 43–80] as a combinatorial representation of the acting semigroup. In this paper, we first study some algebraic p...

To enrich the interplay between a near-Γ-semiring and its operator seminearrings which have been started in (Sardar and Mukherjee, 2014), in this paper at first an order isomorphism between the poset of all Γ-near-ring congruences on a near-Γ-semiring and the poset of all of its normal full k-ideals has been established. Using that result together...

In order to find an analogue of the structure theorem,“a semigroup is a full subdirect product of a semilattice and a group if and only if it is an [Formula: see text]-inversive sturdy semilattice of cancellative monoids (Theorem 14 of [H. Mitsch, Subdirect products of E-inversive semigroups, J. Austral. Math. Soc. 48 (1990) 66–78])”, in the settin...

The bijections (i) between the set of all near-ring congruences on a seminearring S and the set of all generalised strong dense reflexive right k-ideals and (ii) between the set of all zero-symmetric near-ring congruences on a seminearring S and the set of all generalised strong dense reflexive k-ideals established in Theorems 5 and 6 (Chakraborty,...

In this paper we define C-induced action graph G(S, a, C; A) corresponding to a semigroup act (S, a, A) and a subset C of S. This generalizes many interesting graphs including Cayley Graph of groups and semi-groups, Transformation Graphs (TRAG), Group Action Graphs (GAG), De-rangement Action Graphs, Directed Power Graphs of Semigroups etc. We focus...

While establishing the bijection between near-ring congruences and various types of ideals of seminearrings, different kinds of restrictions were imposed either on the seminearrings under consideration or on the near-ring congruences. In this paper we consider a seminearring S without any restriction and establish that there exists an inclusion pre...

As a continuation of the work done in (R. Mukherjee (Pal), P. Pal and S. K. Sardar, On additively completely regular seminearrings, Commun. Algebra45(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 (...

There are four algebraic structures in a Morita context R, S,R PS,S QR, θ, φ , two semirings R, S and two semimodules P , Q. There is a nice interplay among these components which is evident from the study accomplished by Katsov et al. [10] and Sardar and Gupta [8, 12]. The main purpose of this paper is to extend the above mentioned studies by obta...

There are four algebraic structures in a Morita context. There is nice interplay among the components of a Morita context which is evident from the study accomplished by Laan et al. [11], Gupta et al. [8] and Sardar et al. [18]. Among other things, connection between different types of lattices of various pairs of components of a Morita context hav...

In this paper we introduce the notion of (bi) linked group congruence on a (bi) linked semigroup. Inclusion preserving bijection between the set of all (bi) linked group congruences and the set of all dense k-ideals has firstly been obtained. Subsequently these results have been refined to lattice isomorphisms. For a linked semigroup (S, T, f) (bi-...

In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if an...

As a continuation of our previous work, an attempt has been made to obtain some sort of analog of structure theorem of Clifford semigroups in the setting of seminearrings. To accomplish this, the notion of strong bisemilattice of seminearrings has been introduced. Then those left (right) Clifford seminearrings, which are strong bi-semilattice of ne...

In an attempt to investigate the situation arising out of replacing additive regularity by additive complete regularity in our previous study on additively regular seminearrings, we introduce the notions of left (right) completely regular seminearrings and characterize left (right) completely regular seminearrings as bi-semilattices of left (resp.,...

In the class of natural seminearrings i.e., the seminearrings of all self-maps of additive semigroups, the additively regular seminearrings are precisely the seminearrings of self-maps of additively regular semigroups. Hence there are plenty of natural seminearrings which are not additively regular. In this paper we consider a restricted type of su...

The most natural seminearrings, i.e., the seminearrings of all self-maps of additive semigroups are necessarily multiplicatively regular but they need not be additively regular. The purpose of this paper is to investigate additively regular seminearrings. We mainly focus on the study of congruences in various types of additively regular seminearrin...

In order to study near-Γ-semirings the notion of operator seminearrings of a near-Γ-semiring are introduced. Then we obtain an inclusion preserving bijection between the set of all weak ideals of a near-Γ-semiring and that of its left operator seminearring. We also obtain an inclusion preserving bijection between the set of all ideals of a near-Γ-s...

We first obtain results of fuzzy operands of semigroups. Then some nice interplays between operands M of a semigroup and its fuzzy suboperands are obtained in terms of decomposition. These are then used to revisit one important result of semigroup operands viz. “there exists a bijection between the set of all decompositions of a right operand M ove...

The most natural seminearrings, i.e., the seminearrings of all self-maps of additive semigroups are necessarily multiplicatively regular but they need not be additively regular. The purpose of this paper is to investigate additively regular seminearrings. We mainly focus on the study of congruences in various types of additively regular seminearrin...

In this paper a correspondence between the set of all intuitionistic fuzzy ideals of a Γ-semiring and the set of all intuitionistic fuzzy ideals of its operator semirings is established and used them to study some properties of the semiring S_{2}.

Using fuzzy points the notions of prime fuzzy ideals, weakly prime fuzzy ideals, completely prime fuzzy ideals, and weakly completely prime fuzzy ideals of a po-Γ-semigroup have been introduced. Some important properties and characterizations of these ideals have been obtained. The relations among various types of primeness have also been investiga...

In this paper the notions of fuzzy ideals of a po-􀀀-semigroup have been introduced and some of their important properties have been investigated. A characterization of regular po-􀀀-semigroup has been obtained. Various rela- tionships between fuzzy ideals of a po-􀀀-semigroup and those of its operator po- semigroups have also been obtained.

The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained.

In this paper, semilattice congruence and fuzzy semilattice congru-ence on po-Γ-semigroup are studied via operator semigroups. Among other results we obtain a lattice isomorphism between fuzzy semilattice congruences of a Γ-semigroup and that of its left operator semigroup. Using this result we have shown that any sublattice of the lattice of all f...