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Smarandache Semirings, Semifields, And Semivector Spaces

By W. B. Vasantha Kandasamy

Book Id: WPLBN0002097644
Format Type: PDF eBook:
File Size: 0.7 MB
Reproduction Date: 9/14/2011

 Title: Smarandache Semirings, Semifields, And Semivector Spaces Author: W. B. Vasantha Kandasamy Volume: Language: English Subject: Collections: Historic Publication Date: 2002 Publisher: American Research Press Member Page: Florentin Smarandache Citation APA MLA Chicago B. Vasantha Kandasam, B. W. (2002). Smarandache Semirings, Semifields, And Semivector Spaces. Retrieved from http://www.self.gutenberg.org/

Excerpt
Smarandache notions, which can be undoubtedly characterized as interesting mathematics, has the capacity of being utilized to analyse, study and introduce, naturally, the concepts of several structures by means of extension or identification as a substructure. Several researchers around the world working on Smarandache notions have systematically carried out this study. This is the first book on the Smarandache algebraic structures that have two binary operations. Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure — for all rings and fields are semirings. The study of this concept is very meagre except for a very few research papers. Now, when we study the Smarandache semirings (S-semiring), we make the richer structure of semifield to be contained in an S-semiring; and this S-semiring is of the first level. To have the second level of S-semirings, we need a still richer structure, viz. field to be a subset in a S-semiring. This is achieved by defining a new notion called the Smarandache mixed direct product. Likewise we also define the Smarandache semifields of level II. This study makes one relate, compare and contrasts weaker and stronger structures of the same set.