P-(S. P) Submodules and C1(Extending) Modules

Submodules of Secondary Modules

MODULES FOR Z/p× Z/p

We investigate various aspects of the modular representation theory of Z/p × Z/p with particular focus on modules of constant Jordan type. The special modules we consider and the constructions we introduce not only reveal some of the structure of (Z/p× Z/p)-modules but also provide a guide to further study of the representation theory of finite group schemes.

Pure Submodules of Multiplication Modules

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...

δ-Small Submodules and δ-Supplemented Modules

Similar Submodules and Coincidence Site Modules

We consider connections between similar sublattices and coincidence site lattices and, more generally, between similar submodules and coincidence site modules of general (free) Z-modules in R. In particular, we generalise results obtained by S. Glied and M. Baake on similarity and coincidence isometries of lattices and certain lattice-like modules called S-modules. An important result is that t...