10 papers · 1 filter
Primitive hyperideals and hyperstructure spaces of hyperrings
Bijan Davvaz, Amartya Goswami, Karin-Therese Howell
We introduce primitive hyperideals of a hyperring R and show relations with R itself, and with maximal and prime hyperideals of R. We endow a Jacobson topology on the set of primit…
Spectral topologies on skew braces
Themba Dube, Amartya Goswami
Using a new definition of a prime ideal of a skew brace A, on set Spec A of prime ideals of A we endow a spectral topology (in the sense of Grothendieck). We characterize irreducib…
Iséki spaces of semirings
Amartya Goswami
The aim of this paper is to study Iseki spaces of distinguished classes of ideals of a semiring endowed with a topology. We show that every Iséki space is quasi-compact whenever th…
Normal structure spaces of groups
Amartya Goswami
Can we do a topological study of various classes of normal subgroups endowed with a hull-kernel-type topology? In this paper, we have provided an answer to this question. We have i…
Jacobson program for Lie algebras
Amartya Goswami
Following the structure theory approach for rings, the aim of this paper is to study some distinguished classes of Lie algebras. We introduce the notion of a Lie-module and discuss…
Multidimensional population modeling with transition structures
Amartya Goswami
The aim of this paper is to describe a population model with transition. We analyze the spectral properties of the transition matrix considering both irreducible and reducible stru…
Primitive ideals and Jacobson's structure spaces of noncommutative semigroups
Amartya Goswami
The purpose of this note is to introduce primitive ideals of noncommutative semigroups and study some topological aspects of the corresponding structure spaces.
Distinguished classes of ideal spaces and their topological properties
Carmelo A. Finocchiaro, Amartya Goswami, Dario Spirito
We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of…
Proper spaces are spectral
Amartya Goswami
Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we intend to show that the set of proper ideals of a ring endowed with coarse lower top…
Ideal spaces: An extension of structure spaces of rings
Themba Dube, Amartya Goswami
Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but no…