Some Studies on Generalized Alternative Rings.

      Аннотация: The modern structure of algebra is developed three concepts that includes Group, Ring, and Field commonly known to be GRF. Rings is an algebraic structure and possess operations similar to the field but it does not enclose the division operation necessarily.The present study is on the non-associative rings, which belong to the important concept of rings in Algebra. The present work on non-associative rings involves the characterization of rings through different lemma and theories. The work also discussed about the alternativity, commutativity, associativity, and nil-potency of the non-associative alternative rings. The extensive literature review is carried out on the evolution of the non-associative rings and also highlights the research on non-associative rings along with its various forms and identities.The study on non-associative rings yielded several interesting algebraic outcomes. The main work begins with the discussion and proofing of the commutativity of non-associative rings with some relations.

Ключевые слова: algebra, Rings, Associative Rings, Non Associative rings, fields