Searched over 7.2 Billion pages in 1.38 seconds
Please wait while the eBook Finder searches for your request. Searching through the full text of 2,850,000 books. Full Text searches may take up to 1 min.
... Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co. (Seattle, Washington State... ... at: http://PublishingOnline.com This book has been peer reviewed and recommended for publication by: Dr. M. Khoshnevisan, Sharif University... ...gton, Texas 76019, USA. Copyright 2002 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many bo... ...i) The greatest amongst the lower bounds whenever it exists is called the infimum of B, and is denoted by inf B. iv) The least upper bound of B, whe... ...y inf B. iv) The least upper bound of B, whenever it exists is called the supremum of B and is denoted by sup B. DEFINITION 1.3.5: A poset (L, ≤... ...12 S-loop, 59, 98 surjective, 13 I Idempotent law, 12 122 Infimum, 12 Infinite loop, 15 Injective homomorphism, see Homomorphism, ... ...tice, sub-lattice Subloop, 7, 11, 15, 17-21, 24-25, 35-37, 39, 47-49, 51 Supremum, 12 Surjective homomorphism, see Homomorphism, surjective Sylow ...
...e properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate texts and as advanced research books....
... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXIS Church Rock 20... ...AL MAPS HEXIS Church Rock 2004 1 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy De... ...SA Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co. (Seattle, Washingt... ...ds, every other lower bound of A, then it is called the greatest lower bound or infimum, of A. If a particular upper bound proceeds every other uppe... ... exist the largest solution for the set of solution is not closed set i.e. the supremum of the solutions does not give unique output. Kagei [42] wr... ...r ∀ for which generalization ∀x with respect to all x ∈ ℵ means to consider the infimum of the corresponding truth degrees: [ [ ∀xH(x) ]] = de... ...to one, so that µ A (x) t µ R (x, y) = µ A (x) < µ B (y). It is obvious the supremum is an element of the set {(x, y)| µ A (x) ≥ µ B (y)}. That ... ...main. The application of a relation on a given input membership function is a supremum process over the support of A. Because of the monotonicity ... ...6 I Implication, 110 Inefficient solution, 261 Inefficient solution, 59 Infimum, 25 Integral fuzzy neutrosophic column vector, 245 Integral...
...The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though we have a comprehensive bibliography, we do not promise to give all the possible available literature about FRE and its applicati...
...epicting the classical algebraic structures with single binary operations and their Smarandache analogues. The pictures on the left, composed of con... ...ntric circles, depicts the traditional conception of algebraic structures, and the pictures of the right, with their liberal intersections, describe ... ...that the world of classical mathematics – was a little too much of a black and white world, that the principle of the 'excluded middle' meant that ev... ...⊂ P 1 ⊂ P 2 ⊂ …⊂ P n is called a chain of prime ideals of length n. The supremum of the lengths of all chains is called the dimension of R . DE... ...hen K J ⊆ . iii. K J K J ∩ = ∩ . iv. If J : R → L is a fuzzy ideal with supremum property then ( ) α α J J = . v. If P : R → L is prime then P P ... ...→ L is prime then P P = . vi. If Q : R → L is a primary fuzzy ideal with supremum property then Q is the smallest prime fuzzy ideal containing Q. ... ... λ ∩ µ and the join λ ∪ µ the arbitrary supremum ∪ λ i and the arbitrary infimum ∩ λ i can be verified to have the following formulas. i. (λ ∩ ... ...subgroup µ . On the other hand a fuzzy subgroup may or may not attain its infimum. We shall write in short inf µ for ) x ( inf G x µ ∈ and refer to... ...zzy subsemigroup as in case of a fuzzy subgroup may or may not attain its infimum. We shall write inf µ P for ) x ( P P x inf µ ∈ and refer to it a...
... w. b. vasantha kandasamy smarandache semirings, semifields, and semivector spaces a... ...{d,c} {a,b,d} {a,d,c} {b,d,c} 1 Smarandache Semirings, Semifields, and Semivector spaces W. B. Vasantha Kandasamy Department of Math... ... Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co. (Seattle, Washington Sta... ...ii) The greatest amongst the lower bounds, whenever it exists is called the infimum of B, and is denoted by inf B. iv) The least upper bound of B wh... ...d by inf B. iv) The least upper bound of B whenever it exists is called the supremum of B and is denoted by sup B. Now with these notions and not...
...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 ...
...t ring R = Z 3 × Z 12 × Z 7 . This is a major difference between a ring and a Smarandache ring. For, in a ring the lattice representation of ideal... ... Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co. (Seattle, Washington State... ...blishingOnline.com Peer reviewers: Ion Goian, Department of Algebra and Number Theory, University of Kishinev, Moldova. Sebastian Martin Ruiz... ...c) The greatest amongst the lower bounds whenever it exists is called the infimum of B, and is denoted by inf B. d) The least upper bound of B, w... ...nf B. d) The least upper bound of B, whenever it exists, is called the supremum of B and is denoted by sup B. DEFINITION 1.3.5: A poset (L, ≤...
...Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative p...