منابع مشابه
Subring depth below an ideal
A minimum depth is assigned to a ring homomorphism and a bimodule over its codomain. When the homomorphism is an inclusion and the bimodule is the codomain, the recent notion of depth of a subring in a paper by Boltje-Danz-Külshammer is recovered . Subring depth below an ideal gives a lower bound for BDK’s subring depth of a group algebra pair or a semisimple complex algebra pair.
متن کاملSubring Depth, Frobenius Extensions, and Towers
The minimum depth d B,A of a subring B ⊆ A introduced in the work of Boltje, Danz and Külshammer 2011 is studied and compared with the tower depth of a Frobenius extension. We show that d B,A < ∞ if A is a finite-dimensional algebra and B has finite representation type. Some conditions in terms of depth and QF property are given that ensure that the modular function of a Hopf algebra restricts ...
متن کاملThe Depth of Powers of an Ideal
We study the limit and initial behavior of the numerical function f(k) = depthS/I. General properties of this function together with concrete examples arising from combinatorics are discussed.
متن کاملThe Depth of an Ideal with a given Hilbert Function
Let A = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K with each deg xi = 1. Let I be a homogeneous ideal of A with I 6= A and HA/I the Hilbert function of the quotient algebra A/I. Given a numerical function H : N → N satisfying H = HA/I for some homogeneous ideal I of A, we write AH for the set of those integers 0 ≤ r ≤ n such that there exists a homogeneous ideal ...
متن کاملOn Counting Subring-Subcodes of Free Linear Codes Over Finite Principal Ideal Rings
Let R be a finite principal ideal ring and S the Galois extension of R of degree m. For k and k, positive integers we determine the number of free S-linear codes B of length l with the property k = rankS(B) and k = rankR(B∩R). This corrects a wrong result [1, Theorem 6] which was given in the case of finite fields.
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2012
ISSN: 1742-6596
DOI: 10.1088/1742-6596/346/1/012010