in this paper we investigate decompositions of submodules in modules over a proufer domain into intersections of quasi-primary and classical quasi-primary submodules. in particular, existence and uniqueness of quasi-primary decompositions in modules over a proufer domain of finite character are proved. proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decomposi...

We study the space of functions on a finite-dimensional vector space over a field of odd order as a module for a symplectic group. We construct a basis of this module with the following special properties. Each submodule generated by a single basis element under the symplectic group action is spanned as a vector space by a subset of the basis and has a unique maximal submodule. From these prope...

In the present paper, the author shows that if a homogeneous submodule M of the Bergman module La(Bd) satisfies PM − ∑ i MziPMM ∗ zi ≤ c N + 1 PM for some number c > 0, then there is a sequence {fj} of multipliers and a positive number c′ such that c′PM ≤ ∑ j Mfj M ∗ fj ≤ PM, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules a...

Finite difference methods are becoming increasingly popular for calculating synthetic seismograms because of the ease with which they can be applied to model the low-frequency response of complex geometries for which no analytical solutions can be derived. In addition to the obvious advances in computing speed and storage capabilities which have made numerical solution of large, realistic geome...

Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.

Spatio-temporal dynamics of excitable media with discrete three-level active centers (ACs) and absorbing boundaries is studied numerically by means of a deterministic three-level model (see S. D. Makovetskiy and D. N. Makovetskii, http://arxiv.org/abs/cond-mat/0410460 ), which is a generalization of the Zykov-Mikhailov model (see Sov. Phys. – Doklady, 1986, Vol.31, No.1, P.51) for the case of t...

By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results. 1. Introduction. Let R b...

We consider the following problem: For a system consisting of two components, the behavior of one component is known as well as the desired global behavior. What should be the behavior of the second component such that the behavior of the composition of the two conforms to the desired behavior ? This problem has been called "submodule construction" or "equation solving"; and in the context of s...