On number of indecomposable modular representations of cyclic $p$-group over finite local ring
نویسندگان
چکیده
منابع مشابه
On Skew Cyclic Codes over a Finite Ring
In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
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Let p be a prime number. A finite Galois extension N/F of a number field F with group G has a normal p-integral basis (p-NIB for short) when O′ N is free of rank one over the group ring O′ F [G]. Here, O′ F = OF [1/p] is the ring of p-integers of F . Let m = p be a power of p and N/F a cyclic extension of degree m. When ζm ∈ F×, we give a necessary and sufficient condition for N/F to have a p-N...
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Indecomposable Schur rings over a cyclic group Zn of order n are considered. In the case n = p, p an odd prime, the total number of such rings was described in terms of Catalan numbers by Liskovets and Pöschel [Discr. Math. 214 (2000), 173–191]. Here, a closed formula is shown for the total number of indecomposable Schur rings over Z2m using Catalan and Schröder numbers. The result is obtained ...
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Let 1c "be a field and A a finite-dimensional 7c-algebra (associative, with 1). AVe consider representations of A as rings of endomorpliisms of finitedimensional 7c-spaces, and thus JL-modules, and we ask for a classification of such representations. More generally, we may consider the following problem: given an abelian category # and simple ( = irreducible) objects F(l),..., B(n) in #, what a...
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Let A be an associative algebra over a field K such that the dimension, [A:P], of A over K is finite. Following the terminology of [8], we shall say that A is of bounded module type if there exists an integer re such that for every indecomposable left A-module M, the inequality [M: K] zí re holds. The algebra A is of finite module type if A has only a finite number of nonisomorphic indecomposab...
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ژورنال
عنوان ژورنال: Prykladni Problemy Mekhaniky i Matematyky
سال: 2018
ISSN: 1810-3022
DOI: 10.15407/apmm2018.16.19-29