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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…
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…
On Union of Regular Near-rings
Rajlaxmi Mukherjee, Tuhin Manna, Kamalika Chakraborty +1
'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting o…
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…
The Talented Monoid of Higher-Rank Graphs with Applications to Kumjian-Pask Algebras
Roozbeh Hazrat, Promit Mukherjee, David Pask +1
Given a row-finite higher-rank -graph , we define a commutative monoid which is a higher-rank analogue of the talented monoid of a directed graph. The talented monoid $…
Conjugate Real Classes in General Linear Groups
Krishnendu Gongopadhyay, Sudip Mazumder, Sujit Kumar Sardar
Let $\F$ be a field with a non-trivial involution . An element $g \in {\rm GL}_n(\F)$ is called -real if it is conjugate to . We prove that for $n \geq…