In algebra, in particular, modules over rings are studied. A module X over a ring A is defined by an abelian group (X, +) and a representation of the ring A in the endomorphism ring of X which is considered as left multiplication : A × X → X by elements of A. Moreover, a natural agreement is presumed between addition and multiplication. With this in mind, the following phrase is interpreted: “A module X over a ring A is described by the quadruple (X, A, +, ·).” Note also that A is referred to as the ground ring of X.
Weitere Kapitel dieses Buchs durch Wischen aufrufen
- Vector Spaces
S. S. Kutateladze
- Springer Netherlands
- Chapter 2
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