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- Title
On the uniform bound of reducibility index of parameter ideals of idealizations.
- Authors
Nam, Pham Hong
- Abstract
Let (R ,) be a Noetherian local ring and M a finitely generated R -module. In this paper, we study the polynomial type and the sequential polynomial type of the idealization R ⋉ M of R and M introduced by Cuong [On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings, Nagoya Math. J. 125 (1992) 105–114] and Nhan-Dung-Chau [A measure for non-sequential Cohen Macaulayness of finitely generated modules, J. Algebra 468 (2016) 275–295], respectively. In addition, we give a uniform bound for the reducibility index of parameter ideals of idealizations whose polynomial type and sequential polynomial type are at most one.
- Subjects
NOETHERIAN rings; LOCAL rings (Algebra); POLYNOMIALS; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 9, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501839