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Construction of nilpotent sloops of class n

1997
*
Discrete Mathematics
*

We give in this paper a

doi:10.1016/s0012-365x(96)00069-6
fatcat:ojokjiswdzbilnx56ctad6ccha
*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. ...##
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Page 761 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

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 ...##
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Smarandache Loops
[article]

2003
*
arXiv
*
pre-print

These types

arXiv:math/0307028v1
fatcat:7ky3j32mnjgzbbamxkeeiqtj3i
*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. ...##
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Geometric Semigroup Theory
[article]

2011
*
arXiv
*
pre-print

Geometric semigroup theory is the systematic investigation

arXiv:1104.2301v1
fatcat:j63pq57qxzf4ziu5fffmiybvsm
*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 ...##
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Page 525 of Mathematical Reviews Vol. , Issue Subject Index
[page]

*
Mathematical Reviews
*

*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. ...

##
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Page 434 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

(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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SMARANDACHE NON-ASSOCIATIVE RINGS Smarandache Non-associative rings

2002
*
Standard Address Number
*
unpublished

Thus the study

fatcat:3lwav6noufd7jauqfttpg5thia
*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 ...##
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VASANTHA KANDASAMY Standard Address Number: 297-5092 PRINTED

*
THE UNITED STATES OF AMERICA
*
unpublished

A 5 2 The picture on the cover represents the lattice

fatcat:rjyecyit5fbtzdxwv23ibgbhju
*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. ...##
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BIALGEBRAIC STRUCTURES AND SMARANDACHE BIALGEBRAIC STRUCTURES AMERICAN RESEARCH PRESS 5 4 2 3 0 1 Bialgebraic Structures and Smarandache Bialgebraic Structures

2003
unpublished

Now we have given methods

fatcat:x4y4x3ey2jdrxpulvuf2pnf7eu
*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, [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [161] [162] [163] [164] 137, 143, 155, 161, [175] [176] [177 ...##
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S P R I N G 2 0 0 8 arts SCIENCE AND whereAREYOU? Answer found on the back cover

unpublished

Vanderbilt University is committed to principles

fatcat:juss45oiondexbxip6xcazn3li
*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. ...