O'Reilly logo

Algebra: Abstract and Modern by U. M. Swamy, A. V. S. N. Murthy

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

13

Modules and Vector Spaces

Another important algebraic structure is that of a module over a ring, in particular, a vector space over a division ring or a field. Till now, we have come across groups and rings, where one or two binary operations are involved. Modules are concerned with one binary operation and several binary operations, one corresponding to each element in the ring. Consider an abelian group (M, +) and let R = End(M, +), the set of all endomorphisms of (M, +). It is well known that R is a ring under point-wise addition and composition of mappings ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required