Given a ring of ternions R, i. e., a ring isomorphic to that of upper triangular 2×2 matrices with entries from an arbitrary commutative field F , a complete classification is performed of the vectors from the free left R-module R, n ≥ 1, and of the cyclic submodules generated by these vectors. The vectors fall into 5 + |F | and the submodules into 6 distinct orbits under the action of the gene...

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 ...

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 commutative ring with non-zero identity and m be a unital r-module. then the concept of quasi-secondary submodules of m is introduced and some results concerning this class of submodules is obtained