12 papers · 1 filter
On ideals in quantales -- I
Amartya Goswami
Taking a ring-theoretic perspective as our motivation, the main aim of this series is to establish a comprehensive theory of ideals in commutative quantales with an identity elemen…
Terminal spaces of monoids
Amartya Goswami
The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to stro…
Topological properties of some classes of submodules
Amartya Goswami
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of…
Some aspects of -ideals of semirings
Themba Dube, Amartya Goswami
The aim of this paper is to study some distinguished classes of -ideals of semirings, which include -prime, -semiprime, -radical, -irreducible, and -strongly irre…
Subtractive spaces of semirings
Amartya Goswami
Using the closure operator that defines a subtractive ideal of a semiring , in this note we introduce a topology on the set of all ideals of induced by that operator. We sho…
Novikov algebras and their primitive ideals
Aditya Dwarkesh, Amartya Goswami
The aim of this paper is to study the primitive ideals of Novikov algebras. In terms of modular maximal right ideals, a characterization of the primitive ideals of a Novikov algebr…
Some classes of subsemimodule spaces
Amartya Goswami
The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are . When…
Some remarks on the ring of arithmetical functions
Amartya Goswami
The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we…
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…
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…