groupoids and smarandache groupoids - w kandasamy

... Ivan Nivan and H.S.Zukerman, Introduction to number theory, Wiley Eastern Limited, (1989). 3. W. B. Vasantha Kandasamy, Smarandache Groupoids, http://www.gallup.unm.edu/ ~smarandache /Groupoids. pdf ... the new automaton and ss BandA , the Smarandache free groupoids so that K = (Z, ),,B,A ssss λδ is the new automaton got from K and K is strictly contained in s...

Ngày tải lên: 31/03/2014, 16:18

... loop has a S-subloop; other wise we have the concept of Smarandache pseudo representations only when L is a S-loop. Thus when L is not a S-loop we do not have any Smarandache representation for ... Smarandache Lagrange criteria II (S-Lagrange criteria II) and Smarandache Sylow criteria II. We define these two concepts and leave all the properties about S-loops II to the reader....

Ngày tải lên: 31/03/2014, 15:06

... a 2 a 1 = 0. We define Smarandache f-rings as follows. D EFINITION 3.10.40 : Let R be a ring. Let A be a S-subring of R. R is said to be a Smarandache f-ring (S-f-ring) if and only if A ... As our main motivation for writing this book is to obtain all possible Smarandache analogous in ring we want to see how the collection of Smarandache ideals and Smarandache subrings...

Ngày tải lên: 31/03/2014, 15:06

... semigroups, Smarandache p-Sylow subgroups, Smarandache subsemigroups, Smarandache hyper subsemigroups Smarandache simple semigroups and Smarandache Cauchy semigroup. Finally, the concept of Smarandache ... Therefore, since y -1 = (nx) -1 = x -1 n -1 , y -1 ay = x -1 n -1 anx = x -1 n -1 nax = x -1 ax, whence x and y result in the same...

Ngày tải lên: 31/03/2014, 16:18

... B t } is an ordered basis for W. 24 We say the sum W = W 1 + … + W t is direct or that W is the direct sum of W 1 , …, W t and we write W = W 1 ⊕ …⊕ W t . This sum is referred to as ... 1.1.8: If W 1 and W 2 are finite dimensional subspaces of a vector space V then W 1 + W 2 is finite dimensional and dim W 1 + dim W 2 = dim (W 1 ∩ W 2...

Ngày tải lên: 31/03/2014, 15:04

... subseminear-ring we call N a Smarandache maximal seminear-ring (S-maximal seminear-ring). T HEOREM 6.1.4: If (N, +, .) is a S-maximal seminear-ring then N is a S-seminear- ring. Proof: Follows ... ' ∗ '. Now we proceed on to define free groupoid and Smarandache free groupoid as the notion of these concepts will be used in the construction of Smarandache semi- au...

Ngày tải lên: 31/03/2014, 15:06

... Vol. 14, 4 7-9 9, 1994. 17. Vasantha Kandasamy, W. B. Smarandache Semirings and Semifields. Smarandache Notions Journal, Vol. 7, 1-2 -3 , 8 8-9 1, 2001. http://www.gallup.unm.edu/ ~smarandache/ SemiRings.pdf ... Structures. Bulletin of Pure and Applied Sciences, Delhi, Vol. 17 E, No. 1, 11 9-1 21, 1998. http://www.gallup.unm.edu/ ~smarandache/ ALG-S-TXT.TXT 28...

Ngày tải lên: 31/03/2014, 15:06

... of the wound, singeing of the hair, scorching of the skin and clothing, show that the weapon was fired at close quarters, whilst blackening of the hand points to suicide. Even when the weapon is ... judicial hanging). When the injury is below the fourth, the diaphragm continues forcibly in action, but the lungs are imperfectly expanded, and life will not be maintained for more than a day...

Ngày tải lên: 17/02/2014, 07:20

... We give some important results about S -groupoids and groupoids and S -groupoids, which satisfy special identities like Bol, Bruck, Moufang and alternative. For more about groupoids and S -groupoids ... then we say the S-semigroup is Smarandache weakly commutative (S-weakly commutative). If every proper subset which is subgroup is cyclic then we call S a Smarandache c...

Ngày tải lên: 31/03/2014, 15:02