Block Decomposition For Modules

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International Electronic Journal of Algebra
Volume:22 Issue:22
Block Decomposition For Modules

Block Decomposition For Modules

Pages : 187-201

View : 13 | Download : 11

Publication Date : 2017-07-11

Article Type : Research Paper

Abstract :Block decomposition for rings has been introduced and shown to be unique in the literature insert ignore into journalissuearticles values(see [T. Y. Lam, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 1991]);. Applying annihilator submodules, we extend this definition to modules and show that every module $M$ has a unique block decomposition $M=\bigoplus_{i=1}^nM_i$ where each $M_i$ is an annihilator submodule. We also show that the block decomposition for any ring $R$ and the block decomposition for the module $R_R$, are identical. Block decomposition provides us with a decomposition for $\edmp{M}$ because $\edmp{M}\iso\prod_{i=1}^n\edmp{M_i}$.
Keywords : Annihilator, block orthogonal

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