In this book authors study the new notion of the algebraic structure of the subset semirings using the subsets of rings or semirings. This study is innovative and interesting for the authors feel giving algebraic structure to collection of sets is not a new study, for when set theory was introduced such study was in vogue. But a systematic development of constructing algebraic structures using subsets of a set is absent, except for the set topology and in the construction of Boolean algebras. The authors have explored the study of constructing subset algebraic structures like semigroups, groupoids, semirings, non commutative topological spaces, non associative topological spaces, semivector spaces and semilinear algebras. We have constructed semirings using rings of both finite and infinite order. Thus using finite rings we are in a position to construct infinite number of finite semirings both commutative as well as non commutative. It is important to keep on record we have mainly distributive lattices of finite order which contribute for finite semirings. However this new algebraic structure helps to give several finite semirings. This is the advantage of using this new algebraic structure.
Educational Publisher Inc., Ohio
algebraic structure, subset semirings, neutrosophic logic
W.B. Vasantha Kandasamy & F. Smarandache. Subset Semirings. Ohio: Educational Publishing, 2013.
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