Author
Sugato Gupta
Bio: Sugato Gupta is an academic researcher from Jadavpur University. The author has contributed to research in topics: Morita equivalence & Semiring. The author has an hindex of 3, co-authored 5 publications receiving 20 citations.
Papers
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TL;DR: In this paper, it was shown that the left and right operator semiring of a Nobusawa Γ-semiring with unities are Morita equivalent, and the converse was also deduced.
Abstract: We show that the left operator semiring and the right operator semiring of a Nobusawa Γ-semiring with unities are Morita equivalent. The converse is also deduced, i.e., for two Morita equivalent semirings L and R, a Nobusawa Γ-semiring A with unities is constructed such that the left and right operator semirings of A are isomorphic to L and R, respectively. As an application we first establish a relationship between Morita equivalence and Morita context of semirings, and then enumerate some properties of semirings which remain invariant under Morita equivalence.
7 citations
TL;DR: In this article, the authors revisited the notion of ideal lattices and congruence lattices being preserved by Morita equivalence of semirings, which was originally obtained implicitly by Katsov and his co-authors.
Abstract: In this paper we revisit that ideal lattices and congruence lattices are preserved by Morita equivalence of semirings which is originally obtained implicitly by Katsov and his co-authors. This is then used to obtain some Morita invariants for semirings.
7 citations
TL;DR: In this paper, the counterparts of most of the results on Morita invariants of semirings for semimodules are investigated and the lattice isomorphisms between the s...
Abstract: The purpose of this paper is to investigate the counterparts of most of our results on Morita invariants of semirings for semimodules. Among others, we obtain the lattice isomorphisms between the s...
4 citations
TL;DR: In this paper, it was shown that important ideals such as prime ideals, nil ideals and primary ideals remain invariant under strong Morita equivalence of semigroups with weak local units.
Abstract: In this paper we observe that important ideals like prime ideals, nil ideals, nilpotent ideals, primary ideals etc. remain invariant under strong Morita equivalence of semigroups with weak local units. As a consequence, some radicals and important properties are found to be invariant. Finally, lattice isomorphisms between the set of all ideals and the set of all sub-biacts corresponding to a Morita context of the said class of semigroups are established.
3 citations
06 Feb 2018
TL;DR: In this paper, the notion of Gabriel topology on semirings as well as on bisemimodules with unities was introduced, and it was shown that there is a lattice isomorphism between the Gabriel topologies on semi-irings and those connected via Morita context.
Abstract: In this paper we introduce the notion of Gabriel topology on semirings as well as on bisemimodules with unities. We also show that there is a lattice isomorphism between the Gabriel topologies on semirings and those on bisemimodules connected via Morita context.
2 citations
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TL;DR: In this article, the authors define firm semigroups and firm acts as non-additive analogues of firm rings and firm modules, and show that the categories of firm right acts over two firms are equivalent if and only if they are strongly Morita equivalent, which means that they are contained in a unitary Morita context with surjective mappings.
7 citations
TL;DR: In this paper, the counterparts of most of the results on Morita invariants of semirings for semimodules are investigated and the lattice isomorphisms between the s...
Abstract: The purpose of this paper is to investigate the counterparts of most of our results on Morita invariants of semirings for semimodules. Among others, we obtain the lattice isomorphisms between the s...
4 citations
TL;DR: In this article, it was shown that if two semigroups are connected by an acceptable Morita context, then there is an isomorphism between the quantales of unitary ideals of these two groups.
Abstract: We study properties of the lattice of unitary ideals of a semigroup. In particular, we show that it is a quantale. We prove that if two semigroups are connected by an acceptable Morita context then there is an isomorphism between the quantales of unitary ideals of these semigroups. Moreover, factorisable ideals corresponding to each other under this isomorphism are strongly Morita equivalent.
2 citations
06 Feb 2018
TL;DR: In this paper, the notion of Gabriel topology on semirings as well as on bisemimodules with unities was introduced, and it was shown that there is a lattice isomorphism between the Gabriel topologies on semi-irings and those connected via Morita context.
Abstract: In this paper we introduce the notion of Gabriel topology on semirings as well as on bisemimodules with unities. We also show that there is a lattice isomorphism between the Gabriel topologies on semirings and those on bisemimodules connected via Morita context.
2 citations
TL;DR: In this paper, the main purpose of the paper is to consider two Morita equivalent semirings R and S via Morita context instead of considering them via the equivalence of the resulting semimodule.
Abstract: The main purpose of the paper is to consider two Morita equivalent semirings R and S via Morita context 〈R,S,RPS,SQR,𝜃,ϕ〉 instead of considering them via the equivalence of the resulting semimodule...
2 citations