2025/12/16 by Singh, Tushar, Ansari, Ajim Uddin, Kumar, Shiv Datt
#13E05 #13E99 #13F25 #16N40 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.14519
In this paper, we introduce the concept of nonnil-S-Laskerian rings, which generalize both nonnil-Laskerian rings and S-Laskerian rings. A ring R is said to be nonnil-S-Laskerian if every nonnil ideal I (disjoint from S) of R is S-decomposable. As a main result, we prove that the class of nonnil-S-Noetherian rings belongs to the class of nonnil-S-Laskerian rings. Also, we prove that a nonnil-S-Laskerian ring has S-Noetherian spectrum under a mild condition. Among other results, we prove that if the power series ring R[[X]] is nonnil-S-Laskerian with S-decomposable nilradical, then R is S-laskerian and satisfies the S-SFT property.