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math.RA2026
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…
math.RA2026
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…
math.RA2025
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…