Continuing our earlier investigation [15] of the essential normality of submodules generated by polynomials, the emphasis of this paper is on submodules of the Drury-Arveson module H n. In the case of two complex variables, we show that for every polynomial q ∈ C[z1, z2], the submodule [q] of H 2 is p-essentially normal for p > 2. In the case of three complex variables, we show that there is a ...

12.1.2. Let M be a module over the integral domain R. (a) Assume that M has rank n and that x1, . . . , xn is any maximal set of linearly independent elements of M . Prove that N is isomorphic to Rn and that the quotient M/N is a torsion Rmodule. (b) Prove conversely that if M contains a submodule N that is free of rank n (i.e., N › Rn) such that the quotient M/N is a torsion R-module then M ha...

A theory T of modules is preserved under extensions if for any submodule A of a module B, B is a model of T as soon as A and B/A are. We give a syntactic characterization of theories of modules preserved under extensions for the case of regular rings and also for the case of complete theory of abelian groups. This answers a question of U. Felgner. ∗This research was partly supported by the Nati...

Let G be a connected reductive subgroup of a complex connected reductive group Ĝ. Fix maximal tori and Borel subgroups of G and Ĝ. Consider the cone LR◦(Ĝ,G) generated by the pairs (ν, ν̂) of strictly dominant characters such that Vν is a submodule of Vν̂ . The main result of this article is a bijective parametrisation of the faces of LR◦(Ĝ,G). We also explain when such a face is contained in ano...

Let G be a connected reductive subgroup of a complex connected reductive group Ĝ. Fix maximal tori and Borel subgroups of G and Ĝ. Consider the cone LR(G, Ĝ) generated by the pairs (ν, ν̂) of dominant characters such that Vν is a submodule of Vν̂ (with usual notation). Here we give a minimal set of inequalities describing LR(G, Ĝ) as a part of the dominant chamber. In way, we obtain results about...

We show that the cyclotomic conjecture on characteristic polynomial of $T$-ramified $S$-split Iwasawa modules, introduced in a previous paper and satisfied by abelian fields, governs $\mathbb Z_\ell $-rank submodule fixed points for

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

The purpose of this paper is to introduce a new concept in module M over ring R, called e∗-essential submodule, which generalization an essential submodule. We will some examples and properties about such that, what the inverse image intersection submodules direct sum submodules. show relationship between submodule Noetherian R-module. Also we define e∗-closed with

The complement operation on modules has not been argued so far as we know. We observe that it plays an important role in software maintenance, as well as join and meet operations. A de nition of a module and operations on them is given in category theoretic terms; we adopt well-known characterization of complement as a left adjoint to join. The de nition is rst given locally and then extended t...

It has been observed by different authors that QTAG-modules behave very much like torsion abelian groups. In this paper, in section 3, we characterize quasi-essential submodules (Theorem 3.9) and further find a characterization for an h-pure submodule to be a direct summand (Theorem 3.11). In section 4, we obtained a necessary and sufficient condition for a submodule to be contained in a minima...