We survey and compare invariants of modules over the polynomial ring and the exterior algebra. In our considerations, we focus on the depth. The exterior analogue of depth was first introduced by Aramova, Avramov and Herzog. We state similarities between the two notion of depth and exhibit their relation in the case of squarefree modules. Work of Conca, Herzog and Hibi and Trung, respectively, ...

Top-down design methodology is one of the widely used approaches to the design of complex concurrent systems. In this approach, the speciication of a system is decomposed into a set of submodules whose concurrent behavior is equivalent to that of the system speciication. The following problem is of particular importance when using this methodology: given the speciication of a system and some of...

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

The weak-* topology is seen to play an important role in the study of various finiteness conditions one may place on a coalgebra C and its dual algebra C*. Here we examine the interplay between the topology and the structure of ideals of 0*. The basic theory has been worked out for the commutative and almost connected cases (see [2]). Our basic tool for reducing to the almost connected case is ...

The Stickelberger elements attached to an abelian extension of number fields conjecturally participate, under certain conditions, in annihilator relations involving higher algebraic K-groups. In [13], Snaith introduces canonical Galois modules hoped to appear in annihilator relations generalising and improving those involving Stickelberger elements. In this paper we study the first of these mod...

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...