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Basic Abstract Algebra by S. K. Jain, S. R. Nagpaul, P. B. Bhattacharya

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CHAPTER 14

Modules and vector spaces

1 Definition and examples

Let M be an additive abelian group, and let End(M) be the ring of endomorphisms of M(Section 3.1(c), Chapter 9). If images, images, then rm will denote the image of m by r. Therefore

(i) r(m1 + m2) = rm1 + rm2,

(ii) (r1 + r2)m = r1m + r2m,

(iii) (r1r2)m = r1(r2m),

(iv) 1m = m,

where images, images.

We then ...

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