Let (W, S) be a finite Coxeter system and A := Z[0] be the group algebra of a finitely generated free abelian group 0. Let H be an Iwahori-Hecke algebra of (W, S) over A with parameters vs . Further let K be an extension field of the field of fractions of A and KH be the extension of scalars. In this situation Kazhdan and Lusztig have defined their famous basis and the so called left cell modul...

we investigate buchbaum and eisenbud's construction of the second symmetric power $s_r(x)$ of a chain complex $x$ of modules over a commutative ring $r$. we state and prove a number of results from the folklore of the subject for which we know of no good direct references. we also provide several explicit computations and examples. we use this construction to prove the following ...

Let M be a free finitely generated Z-module with basis B and ∆M the kernel of the homomorphism M → Z which maps B to 1. A basis of ∆M can be easily constructed from the basis B of M . Let further R be a submodule of M such that N = M/R is free. The subject of investigation is the module ∆N = (∆M + R)/R. We compute the index [N : ∆N ] and construct bases of ∆N with the help of a basis of N . Fin...

Let W (̟k) be the finite-dimensional irreducible module over a quantized affine algebra U ′ q(g) with the fundamental weight ̟k as an extremal weight. We show that its crystal B(W (̟k)) is isomorphic to the Demazure crystal B −(−Λ0 +̟k). This is derived from the following general result: for a dominant integral weight λ and an integral weight μ, there exists a unique homomorphism Uq(g)(uλ⊗ uμ) → V ...

In this paper, we introduce an algebra H from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra H and the quantum affine algebra Uq1/2(ŝl2), where q denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice...

Suppose R and S are local rings and (R,m) → (S,n) is a flat local homomorphism. Given a finitely generated S-module N , we say N is extended (from R) provided there is an R-module M such that S ⊗R M is isomorphic to N as an S-module. If such a module M exists, it is unique up to isomorphism (cf. [EGA, (2.5.8)], and it is necessarily finitely generated. The m-adic completion R → R̂ and the Hensel...

We investigate Buchbaum and Eisenbud's construction of the second symmetric power $s_R(X)$ of a chain complex $X$ of modules over a commutative ring $R$. We state and prove a number of results from the folklore of the subject for which we know of no good direct references. We also provide several explicit computations and examples. We use this construction to prove the following vers...

Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring,  named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists  such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...

Roughness in modules have been investigated by B. Davvaz and M. Mahdavipour in 2006 [5]. The purpose of this paper is to introduce and discuss the concept of T -rough prime and primary submodules which is a generalization the lower and upper approximation submodules over a commutative ring. We define a set-valued homomorphism on a module and study some properties of it . We prove some results f...