Modules whose $p$-submodules are direct summands

Modules whose direct summands are FI-extending

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

Modules Whose Small Submodules Have Krull Dimension

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

Direct Summands of Syzygy Modules of the Residue Class Field

Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the nth syzygy module of the residue class field of R has a non-trivial direct summand of finite Gdimension for some n. It is proved that if n is at most two then it is true, and moreover, the structure of the ring R is determined essentially uniquely.

Submodules of Secondary Modules

Indecomposable Summands of Foulkes Modules

In this paper we study the modular structure of the permutation module H ) of the symmetric group S2n acting on set partitions of a set of size 2n into n sets each of size 2, defined over a field of odd characteristic p. In particular we characterize the vertices of the indecomposable summands of H ) and fully describe all of its indecomposable summands that lie in blocks of p-weight at most tw...