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... AMERICAN RESEARCH PRESS REHOBOTH 2002 A 1 L 15 (8) {e} A 15 B 1 B 5 1 Smarandache Loops W. B. Vasantha Kandasamy Depart... ...1 L 15 (8) {e} A 15 B 1 B 5 1 Smarandache Loops W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technolo... ...(8) {e} A 15 B 1 B 5 1 Smarandache Loops W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madra... ...exas 76019, USA. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can... ...s 76019, USA. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be... ...USA. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be download... ....O., Phillips J.D., Robinson D. A., Solarin A. R. T., Tim Hsu, Wright C.R.B. and by others who have worked on Moufang loops and other loops like Bol ... ... a new class of loops and loop rings, Ph.D. thesis IIT(Madras), guided by Vasantha.W.B., (1994). 57. Smith.J.D.H, Commutative Moufang loops: the f...

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... 1 Bialgebraic Structures and Smarandache Bialgebraic Structures W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Techn... ... Bialgebraic Structures and Smarandache Bialgebraic Structures W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technolo... ...aic Structures and Smarandache Bialgebraic Structures W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madra... ... Nigeria. Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books c... ...geria. Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can ... ... Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be downlo... ...n of time. I also thank my daughters Meena and Kama and my husband Dr. Kandasamy without whose combined help this book would have been impossible... ...inary operation, called the product and denoted by ' ' such that i. a, b ∈ G implies a b ∈ G. ii. a, b, c ∈ G implies (a b) c = a (b c). i... ...a new class of loops and loop rings, Ph.D. thesis IIT (Madras), guided by Vasantha. W.B., (1994). 49. SMARANDACHE, Florentin, Special Algebraic St...

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... american research press rehoboth 2002 { φ} {a} {b} {c} {d} {a,b,c} {a,b,c,d} {a,b} {a,c} {a,d} {b,c} {b,d} {d,c} {a... ... {a,b,c} {a,b,c,d} {a,b} {a,c} {a,d} {b,c} {b,d} {d,c} {a,b,d} {a,d,c} {b,d,c} 1 Smarandache Semirings, Semifields, and Semivector spaces... ... 1 Smarandache Semirings, Semifields, and Semivector spaces W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Tec... ...1 Smarandache Semirings, Semifields, and Semivector spaces W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Techno... ...andache Semirings, Semifields, and Semivector spaces W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Mad... ...ity, India. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can ... ...a. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be downlo... ...rs, Vol. III, Abaddaba, Oradea, 78-81, (2000). 5. Vasantha Kandasamy, W. B. Smarandache Semirings and Semifields, Smaranda... ...III, Abaddaba, Oradea, 78-81, (2000). 5. Vasantha Kandasamy, W. B. Smarandache Semirings and Semifields, Smarandache Notio...

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... American Research Press Rehoboth 2002 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of... ... American Research Press Rehoboth 2002 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Te... ... American Research Press Rehoboth 2002 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology ... ...achers College, China. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many boo... ...ers College, China. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books ... ...ge, China. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be do... ... said to define an equivalence relation on A if (a, a) ∈ S for all a ∈ A (a, b) ∈ S implies (b, a) ∈ S (a, b) ∈ S and (b, c) ∈ S implies that (a,... ... of Pure and Applied Sciences, Delhi, Vol. 17E, No. 1, 119-121, 1998. 2. W.B.Vasantha Kandasamy, Smarandache cosets, Smarandache Notions Journal,... ...and Applied Sciences, Delhi, Vol. 17E, No. 1, 119-121, 1998. 2. W.B.Vasantha Kandasamy, Smarandache cosets, Smarandache Notions Journal, American...

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...d group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Techn... ... group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technolo... ...group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras... ... Indian Institute of Technology Madras Chennai – 600 036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv ... ...tion by: Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books c... ...n by: Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can ... ... Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be downlo... ... DEFINITION 1.2.8: Let µ be a fuzzy subgroup of a group G. Then for any a, b ∈ G a fuzzy middle coset a µ b of the group G is defined by (a µ b) (x) ... ...ps, Ph.D. Thesis, IIT (Madras), June 1998. Research Guide: W. B. Vasantha Kandasamy. 90. MILIC, Svetozar, and TEPAVCEVIC, Andreja, On P-fuzzy corres...

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... REHOBOTH, NM 2002 1 Smarandache Non-associative rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Techn... ...HOBOTH, NM 2002 1 Smarandache Non-associative rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technolo... ...M 2002 1 Smarandache Non-associative rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madra... ...e, Nigeria. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books c... ...Nigeria. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can ... ... Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be downlo... ...port and encouragement made me write this book. I thank my husband Dr. Kandasamy and my daughters Meena and Kama, who tirelessly worked for very ... ...α and β in such a way that a. addition is commutative α + β = β + α . b. addition is associative that is α + ( β + γ) = ( α + β) + γ. c. There i... ...rings, Proc. London Math. Soc., 46, 231-248 (1940). 33. IQBAL UNNISA and VASANTHA KANDASAMY, W. B., Supermodular lattices, J. Madras Univ., 44, 58-...

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...7 a 11 a 9 a 1 a 4 a 15 a 12 a 0 1 Smarandache Rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Techn... ...a 11 a 9 a 1 a 4 a 15 a 12 a 0 1 Smarandache Rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technolo... ... a 1 a 4 a 15 a 12 a 0 1 Smarandache Rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madra... ...sam, India. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can... ..., India. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be... ... Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be download... ... following axioms are satisfied. 1. The set G is non-empty. 2. If a, b, c ∈ G then a(bc) = (ab) c. 3. There are exists in G an element e such t... ...semigroups is very recent one, done by F. Smarandache, R. Padilla and W.B. Vasantha Kandasamy [73, 60, 154, 156], we felt it is appropriate that the ... ... is very recent one, done by F. Smarandache, R. Padilla and W.B. Vasantha Kandasamy [73, 60, 154, 156], we felt it is appropriate that the notion of ...

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... American Research Press Rehoboth 2002 A 1 × A 2 Z 2 Z 1 B 1 × B 2 A 1 A 2 B 1 B 2 4 0 1 2 3 1 W. B. Vasantha ... ... Z 2 Z 1 B 1 × B 2 A 1 A 2 B 1 B 2 4 0 1 2 3 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Tech... ... Z 1 B 1 × B 2 A 1 A 2 B 1 B 2 4 0 1 2 3 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology M... ...ipiona 11550, Spain. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books... ...ona 11550, Spain. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books ca... ..., Spain. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be down... ...l be used in this book. As concerned with notations, the familiar symbols a > b, a ≥ b, |a|, a / b, b / a occur with their usual meaning. DEFINIT... ...man, Introduction to number theory, Wiley Eastern Limited, (1989). 3. W.B. Vasantha Kandasamy, Smarandache Groupoids, http://www.gallup.unm.edu/~... ...oduction to number theory, Wiley Eastern Limited, (1989). 3. W.B. Vasantha Kandasamy, Smarandache Groupoids, http://www.gallup.unm.edu/~smarandac...