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Properties of analogues of Frobenius powers of ideals

Author

Listed:
  • Subhajit Chanda

    (New Academic Complex, IIT Madras)

  • Arvind Kumar

    (Chennai Mathematical Institute)

Abstract

Let $$R=\mathbb {K}[X_1, \ldots , X_n ]$$ R = K [ X 1 , … , X n ] be a polynomial ring over a field $$\mathbb {K}$$ K . We introduce an endomorphism $$\mathcal {F}^{[m]}: R \rightarrow R $$ F [ m ] : R → R and denote the image of an ideal I of R via this endomorphism as $$I^{[m]}$$ I [ m ] and call it to be the m-th square power of I. In this article, we study some homological invariants of $$I^{[m]}$$ I [ m ] such as regularity, projective dimension, associated primes, and depth for some families of ideals, e.g., monomial ideals.

Suggested Citation

  • Subhajit Chanda & Arvind Kumar, 2023. "Properties of analogues of Frobenius powers of ideals," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 524-531, June.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:2:d:10.1007_s13226-022-00272-3
    DOI: 10.1007/s13226-022-00272-3
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