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Properties of analogues of Frobenius powers of ideals
- Source :
- Indian Journal of Pure and Applied Mathematics. 54:524-531
- Publication Year :
- 2022
- Publisher :
- Springer Science and Business Media LLC, 2022.
-
Abstract
- Let $R=\mathbb{K}[X_1, \ldots , X_n ]$ be a polynomial ring over a field $\mathbb{K}$. We introduce an endomorphism $\mathcal{F}^{[m]}: R \rightarrow R $ and denote the image of an ideal $I$ of $R$ via this endomorphism as $I^{[m]}$ and call it to be the $m$ \textit{-th square power} of $I$. In this article, we study some homological invariants of $I^{[m]}$ such as regularity, projective dimension, associated primes and depth for some families of ideals e.g. monomial ideals.<br />9 pages
Details
- ISSN :
- 09757465 and 00195588
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- Indian Journal of Pure and Applied Mathematics
- Accession number :
- edsair.doi.dedup.....f73ea20b9991e90e41dffde3bc19f9e0