let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

Let o be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite o-module M of rank two. The main emphasis is on the interaction between the different groups and their representations. An induction scheme is developed in order to study the whole family of these groups coherently. The results ob...

We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl n and sln, and give a complete reducibility result. These quantum groups have a natural n-dimensional module V . We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the quantum group action on the k-fold ten...

Let V be Euclidean space. Let W ⊂ GL(V ) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H ∈ A choose αH ∈ V ∗ such that H = ker(αH). The arrangement A is known to be free: the derivation module D(A) = {θ ∈ DerS | θ(αH ) ∈ SαH} is a free S-module with generators of degrees equal to the exponents of ...

Two related results are proven in the modular invariant theory of GLn(Fq ). The first is a finite field analogue of a result of Springer on coinvariants of the symmetric group Sn acting on C[x1, . . . , xn]. It asserts that the following two Fqn [GLn(Fq )×F × q ]modules have the same composition factors: • the coinvariant algebra for GLn(Fq ) acting on Fqn [x1, . . . , xn], in which GLn(Fq ) ac...

The main objective of this study was to estimate the genetic parameters for multi-trait evaluation of birth weight (BW), gestation length (GL) and calving difficulty (CD) in first-parity Iranian Holstein dairy cattle. The data included 29,950 calving records collected during 1995 to 2014 by the Animal Breeding and Improvement Center of Iran. A threshold-linear sire-maternal grandsire model was ...