25 papers
Ideals in quantales, II
Amartya Goswami
As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain t…
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…
Homological lemmas for (non-abelian) group-like structures by diagram chasing in a self-dual context
Kishan Kumar Dayaram, Amartya Goswami, Zurab Janelidze +2
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper, we…
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…
-spaces of non-domain-valued geometric points
Amartya Goswami
The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a -algebra and th…
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…
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…
Salamander lemma for non-abelian group-like structures
Amartya Goswami
It is well known that the classical diagram lemmas of homological algebra for abelian groups can be generalized to non-abelian group-like structures, such as groups, rings, algebra…
L-homologies of double complexes
Amartya Goswami
The notion of L-homologies (of double complexes) as proposed in this paper extends the notion of classical horizontal and vertical homologies, along with two other new homologies i…
A Zariski-like topology on the ideal spectrum of a ring
Amartya Goswami
The purpose of this paper is to introduce a Zariski-like topology on the spectrum of all proper ideals of a ring. We show that the space is T_0, quasi-compact, and every irreducibl…