On Strongly Α-Regular Near-Rings - Sharon, D. Nethra; D. Radha, D. Radha (Journal of Neonatal Surgery, 2025)
This paper introduces and studies the concept of strongly α-regular near-rings and investigates their structural properties. New notions of left and right strongly α-regular near-rings are defined and examined in relation to α-regularity. Various results are established connecting strong α-regularity with conditions when like simple, reduced and subdirect irreducible under which α-regular near-rings become strongly α-regular are obtained, and the equivalence between left and right strongly α-regularity is discussed under suitable constraints. The role of idempotent elements and the absence of zero divisors are also explored. Furthermore, examples are provided to illustrate the concepts and to show that certain converses do not hold in general. The results contribute to the development of generalized regularity conditions in near-ring theory and provide a framework for further investigations involving endomorphism-based identities