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On nonnil-zero-divisor rings | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 99-114 اصل مقاله (215.82 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.28466.1715 | ||
| نویسندگان | ||
| S. Visweswaran* 1؛ H. D. Patel2 | ||
| 1Department of Mathematics, Saurashtra University, Rajkot, India | ||
| 2Science and Humanities Department, Government Polytechnic, Bhuj, India | ||
| چکیده | ||
| The rings considered in this paper are commutative with identity and are nonzero. Let R be a ring. An ideal I of R is said to be nonnil if I is not contained in the nilradical of R. We say that R is a nonnil-zero-divisor ring if for any proper nonnil ideal I of R, the set of zero-divisors of the R-module R/I is a finite union of prime ideals of R. This paper aims to discuss some basic properties of nonnil-zero-divisor rings and to compare the ring-theoretic properties of zero-divisor rings with that of the ring-theoretic properties of nonnil-zero-divisor rings. | ||
| کلیدواژهها | ||
| Zero-divisor module؛ Zero-divisor rings؛ Nonnil-zero-divisor rings؛ Nonnil-Noetherian rings؛ Nonnil-Laskerian rings | ||
| مراجع | ||
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