Group Theory and Ring Theory form two enduring pillars of modern algebra, each offering profound insights into symmetry, structure, and operations. Group Theory focuses on the study of sets ...

Algebra and Number Theory are cornerstones of modern mathematics. At their heart, these fields study the underlying structures governing numbers and abstract entities, ranging from rings, fields ...

India’s National Quantum Mission leverages nuclear legacy to lead in quantum computing, communication, sensing, and deep-tech ...

Julian McMahon, ‘Fantastic Four,' ‘Nip/Tuck' and ‘FBI: Most Wanted' Star, Dies at 56 James Carville makes midterms prediction after Trump bill passes ...

This paper presents a novel theoretical approach to the analysis of a ring resonator consisting of an edge-fed circular microstrip of arbitrary width on a substrate over a ground plane; the analysis ...

In this project, we attempt to reformulate various notions from classical commutative algebra (such as flatness, regularity, smoothness, etc.) in an entirely categorical manner, so as to be able to ...

We introduce a new general construction, denoted by R ⋈ E, called the amalgamated duplication of a ring R along an R-module E, that we assume to be an ideal in some overring of R. (Note that, when E 2 ...

We quantitatively study the coupling of ideal modes under perturbation of a ring fiber. Our results indicate that a widely accepted criterion against the coupling of EHm-1,n and HEm+1,n modes may be ...

We explore the concept of the S S -Krull dimension in commutative rings, extending classical notions of Krull dimension by incorporating multiplicative subsets S S of a ring R R. We provide ...