SMARANDACHE NON-ASSOCIATIVE RINGS
| Main Author: | Vasantha, Kandasamy |
|---|---|
| Format: | Book |
| Terbitan: |
, 2002
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/8860 |
Daftar Isi:
- An associative ring is just realized or built using reals or complex; finite or infinite by defining two binary operations on it. But on the contrary when we want to define or study or even introduce a non-associative ring we need two separate algebraic structures say a commutative ring with 1 (or a field) together with a loop or a groupoid or a vector space or a linear algebra. The two non-associative well-known algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space over a field satisfying special identities called the Jacobi identity and Jordan identity respectively. Study of these algebras started as early as 1940s. Hence the study of non-associative algebras or even non-associative rings boils down to the study of properties of vector spaces or linear algebras over fields.