Showing papers by "Sujit Kumar Sardar published in 2016"
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 article, the definition of normal full right k-ideal and normal full kideal can be given as follows and can be considered to be an extension of Definition 310 of [1] Definition 310 (Extended [1]).
Abstract: An error, in Section 3 of our paper [1], has come to our notice recently This can be rectified firstly by replacing throughout the section ‘full right k-ideal’ and ‘full k-ideal’ by ‘normal full right k-ideal’ and ‘normal full k-ideal’, respectively The definitions of normal full right k-ideal and normal full k-ideal can be given as follows and can be considered to be an extension of Definition 310 of [1] Definition 310 (Extended [1]) In an additively inverse seminearring (S,+, ), a full right (left) k-ideal H is said to be normal full right (left) k-ideal if a + h + a∗ ∈ H for all h ∈ H and for all a ∈ S The definition of normal full k-ideal is obvious
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