Nonsingular Zeros of Polynomials Defined Over<i>P</i>-Adic Fields

Chakri, Lekbir; Leep, David B.

doi:10.1080/00927870903389183

Communications in Algebra

2010

DOI: 10.1080/00927870903389183

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Nonsingular Zeros of Polynomials Defined OverP-Adic Fields

Lekbir Chakri

David B. Leep

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Hopf subalgebras and tensor powers of generalized permutation modules

Kadison

2014

Journal of Pure and Applied Algebra

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By means of a certain module V and its tensor powers in a finite tensor category, we study a question of whether the depth of a Hopf subalgebra R of a finite-dimensional Hopf algebra H is finite. The module V is the counit representation induced from R to H, which is then a generalized permutation module, as well as a module coalgebra. We show that if in the subalgebra pair either Hopf algebra has finite representation type, or V is either semisimple with R * pointed, projective, or its tensor powers satisfy a Burnside ring formula over a finite set of Hopf subalgebras including R, then the depth of R in H is finite. One assigns a nonnegative integer depth to V , or any other H-module, by comparing the truncated tensor algebras of V in a finite tensor category and so obtains upper and lower bounds for depth of a Hopf subalgebra. For example, a relative Hopf restricted module has depth 1, and a permutation module of a corefree subgroup has depth less than the number of values of its character.1991 Mathematics Subject Classification. 16D20, 16G60, 16S34, 16T05, 19A22 .

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Hopf subalgebras and tensor powers of generalized permutation modules

Kadison

2014

Journal of Pure and Applied Algebra

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Nonsingular zeros of polynomials defined over finite fields

Chakri¹,

Leep

2021

Communications in Algebra

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Nonsingular Zeros of Polynomials Defined OverP-Adic Fields

Cited by 2 publications

References 2 publications

Hopf subalgebras and tensor powers of generalized permutation modules

Hopf subalgebras and tensor powers of generalized permutation modules

Nonsingular zeros of polynomials defined over finite fields

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