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We give in this paper a construction of nilpotent sloops of class n; for any positive integer n. ... From another direction, we show that the constructed nilpotent sloop can be embedded as a derived sloop of a nilpotent SQS-skein, both are of the same class n. ... The constructed sloop of nilpotence class n can be embedded as a derived sloop of a nilpotent SQS-skein of the same class n. Proof. ...doi:10.1016/s0012-365x(96)00069-6 fatcat:ojokjiswdzbilnx56ctad6ccha
Des. 1 (1993), no. 4, 301- 321; MR 95k:05037] also gave a construction of semi-Boolean SQS-skeins of nilpotence class n whose derived sloops are all of class 1. ... As an extension result, we prove in the present paper the existence of nilpotent SQS-skeins of class n all of whose derived sloops are nilpotent of the same class n, for any positive integer n. 2001b:05052 ...
These types of structures occur in our everyday's life, thats why we study them in this book. ... 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). ... Further by the very construction of the loops in L n (m) ∈ L n , every element in L n (m) is of order two. ...arXiv:math/0307028v1 fatcat:7ky3j32mnjgzbbamxkeeiqtj3i
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. ... In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. ... U LL null semigroups xy = 0 N k nilpotent of class k x 1 · · · x k = 0 COM (m,n) commutative semigroups satisfying x m = x m+n xy = yx, x m = x m+n S variety generated by a finite semigroup S Eqs(S) Z ...arXiv:1104.2301v1 fatcat:j63pq57qxzf4ziu5fffmiybvsm
Nilpotent SQS-skeins with nilpotent derived sloops. (English summary) 2001b:05051 Cho, Jung R. (with Dudek, Jozef) Medial idempotent groupoids. III. ... Representations of q English and Russian summaries) Hsu, Tim Moufang loops of class 2 and cubic forms. ...
(English summary) 98g:53038 20N15 n-ary systems Armanious, M. H. Construction of nilpotent sloops of class n. (English summary) 981:20051 C4ampian, Maria sce Pop, Maria S. ... On constructions of hypergroups. (see 98g:00020) — Constructions of hypergroups. (English summary) 98e:20074 Stratigopoulos, Demetrios Starlike hypergroups of type (m,n). ...
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Thus the study of there two classes of nonassociative rings is carried out in chapters 2 and 3 respectively. and we denote it by o(L) or |L|. ... Example 1.3.1: Let Z + be the set of integers. Define an operation '.' on Z + by a.b = na + mb where m and n are any pair of chosen numbers such that (m, n) = 1 (m ≠ 1, n ≠ 1). ... We have introduced Smarandache Lie concepts only for basic Lie algebras so it remains open for the reader to explore further studies and define new concepts of Smarandache notions in case of Lie superalgebras ...fatcat:3lwav6noufd7jauqfttpg5thia
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A 5 2 The picture on the cover represents the lattice of subgroups of the Smarandache loop L 15 (8). ... But for the Smarandache concepts one wouldn't have studied the collection of subgroups of a loop. ... Further by the very construction of the loops in L n (m) ∈ L n , every element in L n (m) is of order two. ...fatcat:rjyecyit5fbtzdxwv23ibgbhju
Now we have given methods of constructing classes of non-associative birings using groupoids and loops. ... Using the new class of loops L n (m) ∈ L n ; n > 3, n odd and (m, n) = 1 and (m -1, n) = 1, we get a nice class of biloops. ... 196, 213 Near domain, definition of, 43 New class of groupoids, 158,                 137, 143, 155, 161,   [177 ...fatcat:x4y4x3ey2jdrxpulvuf2pnf7eu
Vanderbilt University is committed to principles of equal opportunity and affi rmative action. Cover: Students leave Calhoun Hall after classes. ... John Sloop, associate dean of academic aff airs and professor of communications studies, AXLE helps students avoid creating a narrow educational experience for themselves. ... "I took a history of medicine class. Who would have thought that a class like that even existed for undergraduates? I loved the interdisciplinary nature of MHS. ...fatcat:juss45oiondexbxip6xcazn3li