an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

A family of frequency synthesizers is described. Each member of the family generates one of many equally-spaced frequencies by utilizing identical modules, the number of which is related to the number of possible frequencies. For any design in the family which uses frequency division in the modules, there exists a dual design which utilizes frequency multiplication. Block diagrams and formulas ...

• The Grothendieck ring G0(H) is the abelian group generated by the iso. classes [V ] of finite dim’l (right) H-modules V modulo the relations [V ] = [U ] + [W ] for each s.e.s. 0 → U → V → W → 0. The iso. classes of simple modules form a Z-basis. Multiplication is given by ⊗ = ⊗k. • The character algebra R(H) is the k-subalgebra of H∗ that is generated by the image of the character map χ : G0(...

where the LGLn(λ) are irreducible GLn(C)-modules and the S λ k are irreducible Sk-modules. The decomposition in (0.1) essentially makes the study of the representations of GLn(C) and the study of representations of the symmetric group Sk two sides of the same coin. The group GLn(C) has interesting subgroups, GLn(C) ⊇ On(C) ⊇ Sn ⊇ Sn−1, and corresponding centralizer algebras, CSk ⊆ CBk(n) ⊆ CAk(...

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...

A core operation in actual circuits, especially in digital signal processing algorithms, is multiplication. Often, the computational performance of a DSP system is limited by its multiplication performance [Pet95]. The implementation of multiplier modules into FPGAs is crucial in terms of area, speed and pin limitation. In many cases, even small multiplier modules will exceed the capacity of on...

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Let R be a commutative ring with non-zero identity, S multiplicatively closed subset of and M unital R-module. In this paper, we define submodule N (N :R M) ? = to weakly S-primary if there exists s such that whenever m 0 , am N, then either sa ??(N or sm N. We present various properties characterizations concept (especially in faithful multiplication modules). Moreover, the behavior structure ...

The main goal of this paper is to introduce a new class in the category modules. It called quasi-invertibility monoform (briefly QI-monoform) This modules generalization Various properties and another characterization QI-monoform are investigated. So, we prove that an R-module M if only for each non-zero homomorphism f:M E(M), kernel not quasi-invertible submodule M. Moreover, cases under which...