Let M be a graded leftA-module and M∗ the associate complex of M. Then : If is noetherian (resp. artinian) then strongly hopfian cohopfian); cohopfian), leftA-module, M, N submodule N∗ fully invariant subcomplex M∗. M∗/N∗ hopfian, hopfian. if all cohopfian, cohopfian.

New upper bounds on the first and second Hilbert coefficients of a Cohen-Macaulay module over local ring are given. Characterizations provided for some to be attained. The characterizations given in terms series as well Castelnuovo-Mumford regularity associated graded module.

Graded-CTL is an extension of CTL with graded quantifiers which allow to reason about either at least or all but any number of possible futures. In this paper we show an extension of the NuSMV model-checker implementing symbolic algorithms for graded-CTL model checking. The implementation is based on the CUDD library, for BDDs and ADDs manipulation, and includes also an efficient algorithm for ...

BRST-resolution is studied for the principally graded Wakimoto module of ŝl2 recently found in [9]. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. e-mail:[email protected]

Theorem. Let R be a Cohen-Macaulay ring (locally, always) 1 c R an ideal o f height at least 2, S the Rees ring of R with respect to I, and G = S /S I the associated graded ring. Assume that S and G are Cohen-Macaulay rings, and that S has a canonical module cos. Then G has a canonical module r and: (i) I f co s can be embedded into S such that cos (considered as an ideal now) is not contained ...

Let G be a simple algebraic group over C with the Weyl group W . For a unipotent element u ∈ G, let Bu be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup WL of W . Assume that u ∈ L and let B L u be a similar variety as Bu for L. We describe, for a certain choice of u ∈ L and e ≥ 1, the W -module ⊕ n≡k mod e H2n(Bu) ...

We prove a double-exponential upper bound on the degree and on the complexity of constructing a Janet basis of a D-module. This generalizes a well known bound on the complexity of a Gröbner basis of a module over the algebra of polynomials. We would like to emphasize that the obtained bound can not be immediately deduced from the commutative case. Introduction Let A be the Weyl algebra F [X1, ....

Given a strong deformation retract M of an algebra A, there are several apparently distinct ways ([9],[19], [13], [24],[15], [18], [17]) of constructing a coderivation on the tensor coalgebra of M in such a way that the resulting complex is quasi isomorphic to the classical (differential tor) [7] bar construction of A. We show that these methods are equivalent and are determined combinatorially...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring and $M$ graded $R$-module. In this paper we will obtain some results concerning the generalized 2-absorbing submodules their homogeneous components. Special attention has been paid, when rings are gr-Noetherian, to find extra properties of these submodules.

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over a graded field (with a unit in the appropriate degree). We also classify the ungraded commutative rings for which the category of projective modules admits ...