In this book authors for the first time introduce the notion of non associative vector spaces and non associative linear algebras over a field. We construct non associative space using loops and groupoids over fields. In general in all situations, which we come across to find solutions may not be associative; in such cases we can without any difficulty adopt these non associative vector spaces/linear algebras. Thus this research is a significant one.
This book has six chapters. First chapter is introductory in nature. The new concept of non associative semilinear algebras is introduced in chapter two. This structure is built using groupoids over semifields. Third chapter introduces the notion of non associative linear algebras. These algebraic structures are built using the new class of loops.
Zip Publishing, Ohio
non associative vector spaces, non associative linear algebra, groupoid
W.B. Vasantha Kandasamy & F. Smarandache. NON ASSOCIATIVE LINEAR ALGEBRAS. Ohio: Zip Publishing, 2012.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.