Modules over Noncommutative Rings
A module over an arbitrary ring R is defined in the same way as in the case of a commutative ring: it is a set M such that for any two elements x, y ∈ M, the sum x + y is defined, and for x ∈ M and a ∈ R the product ax ∈ M is defined, satisfying the following conditions (for all x, y, z ∈ M, a, b ∈ R).
KeywordsCommutative Ring Left Ideal Finite Length Group Algebra Division Algebra
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