The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bi...

We investigate representations of the Z22-graded extension osp(1|2), which is spectrum generating algebra recently introduced version superconformal mechanics. The main result a classification irreducible lowest weight modules osp(1|2). This done via introduction Verma and its maximal invariant submodule generated by singular vectors. Explicit formulas all vectors are also presented.

We present an algorithm to compute the primary decomposition of a submodule N of the free module Z[x1, . . . , xn]. For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of N , i.e. the minimal associated primes of the ideal Ann(Z[x1, . . . , xn]/N ) in Z[x1, . . . , xn] and the...

All rings are commutative with 1 6= 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a, b ∈ R and m ∈M and abm ∈ N , then am ∈M -rad(N) or bm ∈M -rad(N) or ...

The modular multilevel converter (MMC) is receiving extensive research interests in high/medium voltage applications due to its modularity, scalability, reliability, high voltage capability and excellent harmonic performance. The submodule capacitors are usually quite bulky since they have to withstand fundamental frequency voltage fluctuations. To reduce the capacitance of these capacitors, th...