6 papers
On structures of the ring of arithmetical functions: prime ideals and beyond
Amartya Goswami, Danielle Kleyn, Kerry Porrill
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…
Spectral spaces of normal subgroups
Amartya Goswami
The aim of this note is to prove that the set of proper normal subgroups of a group endowed with coarse lower topology is a spectral space.
Some results on irreducible ideals of monoids
Amartya Goswami
The purpose of this note is to study some algebraic properties of irreducible ideals of monoids. We establish relations between irreducible, prime, and semiprime ideals. We explore…
Spectrality and monoids
Amartya Goswami
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
On -elements of multiplicative lattices
Themba Dube, Amartya Goswami
The aim of this paper is to investigate further properties of -elements in multiplicative lattices. We utilize -closure operators to extend several properties of -ideals t…
Revisiting Baer elements
Amartya Goswami, Themba Dube
The objective of this paper is to extend certain properties observed in -ideals of rings and -elements of frames to Baer elements in multiplicative lattices introduced in D.…