2025/08/07 by Naseem Ajmal, Ajmal, Naseem, Anand Swaroop Prajapati +1
Computer Science · Decision Sciences · Mathematics · #03G99 #13A99 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2508.14903
openalex publication_date 2025/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the concept of a prime radical of an ideal of an L-ring L(mu,R) . Among various results pertaining to this concept, we prove here that prime radicals of an ideal eta, its radical , its semiprime radical S(eta) and its prime radical P(eta) , all coincide. Also we prove that for a primary ideal, its prime radical coincide with its radical. Moreover, we introduce the concept of primary decomposition and reduced primary decomposition of an ideal in an L-ring. We obtain a necessary and sufficient conditions for an ideal of an L-ring to have a primary decomposition. Some more results pertaining to the decomposition of an ideal are established.