Abstract
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).
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© 2005 Springer-Verlag Berlin Heidelberg
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Shafarevich, I.R. (2005). Modules over Noncommutative Rings. In: Basic Notions of Algebra. Encyclopaedia of Mathematical Sciences, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26474-4_9
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DOI: https://doi.org/10.1007/3-540-26474-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61221-6
Online ISBN: 978-3-540-26474-3
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