ENGLISH

Smarandache Loops

By W. B. Vasantha Kandasamy

Book information

Publisher
American Research Press
Year
2002
ISBN
1931233632, 9781931233637
Open Library ID
OL8802404M
Language
english
Format
PDF
Filesize
541 kB (553584 bytes)
Pages
128\128
Topic
Mathematics Algebra
Library
Techlib
Time added
2009-11-09 02:42:13

Description

In any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S.By proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A.These types of structures occur in our every day’s life, that’s why we study them in this book.As an example:A non-empty set L is said to form a loop, if on L is defined a binary operation called product, denoted by '·', such that:1) For all a, b in L we have a · b in L (closure property);2) There exists an element e in L such that a·e = e·a = a for all a in L (e is the identity element of L);3) For every ordered pair (a, b) in L x L there exists a unique pair (x, y) in L such that ax = b and ya = b.Whence:A Smarandache Loop (or S-loop) is a loop L such that a proper subset M of L is a subgroup (with respect to the same induced operation).

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