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, ...

To each finitely presented module M over a commutative ring R one can associate an R-ideal FitR(M) which is called the (zeroth) Fitting ideal of M over R and which is always contained in the R-annihilator of M . In an earlier article, the second named author generalised this notion by replacing R with a (not necessarily commutative) o-order Λ in a finite dimensional separable algebra, where o i...

Abstract For a semisimple Lie algebra defined over discrete valuation ring with field of fractions K , we prove that any primitive ideal rational central character in the affinoid enveloping algebra, $$\widehat{U({\mathfrak {g}})_{K}}$$ U ( g )</...

Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R. Two distinct vertices I and J are said to be adjacentif and only if I + J = R. In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI Δ J(R), where J(R) denotes the Jacobson radical of R. In this paper westudy about the relation b...

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...

1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal. What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M is strictly cyclic if there exists m in M such that mA = M (such an m is called a generator); a r...