We introduce the concept of "uniformly primary submodules" of a module over a commutative ring R, which generalizes the concept of "uniformly primary ideals" of R, a concept that imposes a certain boundedness condition on the usual notion of "primary ideal". Several results on uniformly primary submodules are proved. Also, we characterize uniformly primary submodules of a multiplication module....

The Springer modules have a combinatorial property called " coincidence of dimensions, " i.e., the Springer modules are naturally decomposed into submodules with common dimensions. Morita and Nakajima proved the property by giving modules with common dimensions whose induced modules are isomorphic to the submodules of Springer modules. They proved that the induced modules are isomorphic to the ...

Specht modules for an Ariki-Koike algebra Hm have been investigated recently in the context of cellular algebras (see, e.g., [GL] and [DJM]). Thus, these modules are defined as quotient modules of certain “permutation” modules, that is, defined as “cell modules” via cellular bases. So cellular bases play a decisive rôle in these work. However, the classical theory [C] or the work in the case wh...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

This paper is concerned with finite unions of ideals and modules. The first main result is that if N ⊆ N1 ∪N2 ∪ · · · ∪Ns is a covering of a module N by submodules Ni, such that all but two of the Ni are intersections of strongly irreducible modules, then N ⊆ Nk for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on co...

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly rings and invertible discuss the relations between these several properties of rings. Also, study concept crossed products some defined product give relationship Moreover, in generalization for essential submodules, semi-uniform modules which is uniform modules.

Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...

We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the...

The algebraic structure of the set of doubly stochastic circulants is that of a semi-ring. The concept of a prime in the doubly stochastic circulants is introduced in this paper and examples are given. The classiication of a prime in the doubly stochastic circulants is equivalent to the solvability of a linear equation over a doubly stochastic circulant. A representation of doubly stochastic ci...