smarandache semirings, semifields,semi vector spaces - w kandasamy

... Semirings and Semifields. Smarandache Notions Journal, Vol. 7, 1-2 -3 , 8 8-9 1, 2001. http://www.gallup.unm.edu/ ~smarandache/ SemiRings.pdf 18. Vasantha Kandasamy, W. B. Smarandache Semigroups, ... http://www.gallup.unm.edu/ ~smarandache/ Vasantha-Book1.pdf 1 Smarandache Semirings, Semifields, and Semivector spaces...

Ngày tải lên: 31/03/2014, 15:06

... in which for all S-subloops we have the same SSZ(L)? 8. Find loop which has many S-subloops but a unique SN(L). 9. Find a S-loop isomorphism of two loops of order 18 and order 28. 4.3 Smarandache ... have like S- loops several S-nuclei II, S-centre II, S-Moufang centre II but unlike loops which has a unique nucleus, centre, Moufang centre and so on. Now one more question is Sma...

Ngày tải lên: 31/03/2014, 15:06

... seminear-ring (S-quotient seminear-ring) of the seminear-ring of N by N / A = {Ax / x ∈ N}. It is not known under what condition N / A will be a near-ring or a S-near-ring or a seminear-ring ... 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. Proo...

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 ... 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 look l...

Ngày tải lên: 31/03/2014, 15:06

... Wiley Eastern Limited, (1989). 3. W. B. Vasantha Kandasamy, Smarandache Groupoids, http://www.gallup.unm.edu/ ~smarandache/ Groupoids.pdf W. B. Vasantha Kandasamy Groupoids and Smarandache ... . Now s K = ), ,B ,A ,Z( sssss δλ is the Smarandache Automaton. A machine equipped with this Smarandache Automaton can use any new automaton as per need. We give so...

Ngày tải lên: 31/03/2014, 16:18

... N(a) in G we claim that x -1 ax ≠ y -1 ay. Were this is not the case, from x -1 ax = y -1 ay, we would deduce that yx -1 a = ayx -1 ; this in turn would imply that yx -1 ∈ N(a). However, this ... (a -1 ) -1 = a. Proof: This simply follows from the fact a -1 • (a -1 ) -1 = e = a -1 • a canceling off the a -1 we get (a -1 )...

Ngày tải lên: 31/03/2014, 16:18

... member of the xy-plane and a member of the yz-plane; here are two such combinations.   w 1 w 2 w 3   = 1 ·   w 1 w 2 0   + 1 ·   0 0 w 3     w 1 w 2 w 3   = 1 ·   w 1 w 2 /2 0   + ... W 3 )? (c) Let W be a subspace of some vector space. Show that W + W = W . (d) Must there be an identity element, a subspace I such that I + W = W + I =...

Ngày tải lên: 25/10/2013, 05:20

... benefits and drawbacks of vector negatio n compared with two other methods for negation. 2 Negation and Disjunction in Vector Spaces In this section we use well-known linear algebra to define vector negation ... Terms were indexed depending on their co-occurrence with 1000 fre quent “content-bearing words” in a 15 word context-window, giving each term 1000 coordinates. This was reduced...

Ngày tải lên: 17/03/2014, 06:20

... 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 cyclic semigroup (S-cyclic ... bigroupoids S-bigroupoids biloops S-biloops binear-rings S-binear-rings birings S-birings bisemigroups S-bisemigroups bisemirings S-bisemigroups bistructures S-bistructures bigroups S-bigro...

Ngày tải lên: 31/03/2014, 15:02

... 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 ... of F. Now we define the notion when are subspaces of a vector space independent. D EFINITION 1.3.5: Let W 1 , …, W m be m subspaces of a vector space V. We say th...

Ngày tải lên: 31/03/2014, 15:04