6 papers
Maximal-Hull -Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings
Pubali Sengupta, Amartya Goswami, Pronay Biswas +1
We develop a spectral theory of -ideals for commutative semirings. The lattice of -ideals is a \emph{coherent frame} for every commutative semiring -- u…
Radical-Ideal Functors, a Support Bifibration, and Quantale Completion for Commutative Semirings
Pronay Biswas, Amartya Goswami, Sujit Kumar Sardar
We organize ordinary, subtractive (-), and strong ideal theory of commutative semirings into a functorial framework. Radical extension is left adjoint to contraction and yields…
On the Subtractive Ideal Structure of Commutative Semirings
Pubali Sengupta, Amartya Goswami, Pronay Biswas +1
In the theory of commutative semirings, the lack of additive inverses creates a structural divergence between ideals and congruences that does not exist in ring theory. The aim of…
The Case for Inverse Semirings
Peter F. Faul, Amartya Goswami, Gideo Joubert +1
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a…
On semisubtractive ideals of semirings
Amartya Goswami
Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their bas…
On -ideals and -closure operations of semirings, I
Amartya Goswami
The aim of this series of papers is to study -ideals of semirings. In this article, we introduce some distinguished classes of -ideals of semirings, which include -prime,…