Zobrazeno 1 - 10
of 117
pro vyhledávání: '"Kinyon, Michael K."'
Publikováno v:
Quasigroups and Related Systems 19 (2011), 239-264
Right groups are direct products of right zero semigroups and groups and they play a significant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left tran
Externí odkaz:
http://arxiv.org/abs/0903.5436
Publikováno v:
Internat. J. Algebra Comput. 19 (2009), no. 8, 1049-1088
Buchsteiner loops are those which satisfy the identity $x\backslash (xy \cdot z) = (y \cdot zx)/ x$. We show that a Buchsteiner loop modulo its nucleus is an abelian group of exponent four, and construct an example where the factor achieves this expo
Externí odkaz:
http://arxiv.org/abs/0708.2358
Publikováno v:
J. Combinatorial Designs 17 (2009), no. 2, 103-118
A commutative loop is Jordan if it satisfies the identity $x^2 (y x) = (x^2 y) x$. Using an amalgam construction and its generalizations, we prove that a nonassociative Jordan loop of order $n$ exists if and only if $n\geq 6$ and $n\neq 9$. We also c
Externí odkaz:
http://arxiv.org/abs/0705.3445
Autor:
Kinyon, Michael K., Vojtechovsky, Petr
Publikováno v:
Comm. Algebra 37 (2009), no. 4, 1428-1444
The decomposition theorem for torsion abelian groups holds analogously for torsion commutative diassociative loops. With this theorem in mind, we investigate commutative diassociative loops satisfying the additional condition (trivially satisfied in
Externí odkaz:
http://arxiv.org/abs/math/0702874
Publikováno v:
Trans. Amer. Math. Soc. 360 (2008), no. 5, 2393-2408
A left Bol loop is a loop satisfying $x(y(xz)) = (x(yx))z$. The commutant of a loop is the set of elements which commute with all elements of the loop. In a finite Bol loop of odd order or of order $2k$, $k$ odd, the commutant is a subloop. We invest
Externí odkaz:
http://arxiv.org/abs/math/0601363
Publikováno v:
Comment. Math. Univ. Carolin. 51 (2010), no. 2, 267-277
In math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show t
Externí odkaz:
http://arxiv.org/abs/math/0601077
Publikováno v:
J. Algebra 317 (2007), 435-461
We solve a problem of Belousov which has been open since 1967: to characterize the loop isotopes of F-quasigroups. We show that every F-quasigroup has a Moufang loop isotope which is a central product of its nucleus and Moufang center. We then use th
Externí odkaz:
http://arxiv.org/abs/math/0510298
We partially answer two questions of Goodaire by showing that in a finite, strongly right alternative ring, the set of units (if the ring is with unity) is a Bol loop under ring multiplication, and the set of quasiregular elements is a Bol loop under
Externí odkaz:
http://arxiv.org/abs/math/0508005
Autor:
Kinyon, Michael K., Kunen, Kenneth
Publikováno v:
J. Algebra 304 (2006), 679-711
We study conjugacy closed loops (CC-loops) and power-associative CC-loops (PACC-loops). If $Q$ is a PACC-loop with nucleus $N$, then $Q/N$ is an abelian group of exponent 12; if in addition $Q$ is finite, then $|Q|$ is divisible by 16 or by 27. There
Externí odkaz:
http://arxiv.org/abs/math/0507278
Publikováno v:
Bul. Acad. Stiinte Repub. Mold. Mat. 3(49) (2005), 71--87.
We describe all constructions for loops of Bol-Moufang type analogous to the Chein construction $M(G,*,g_0)$ for Moufang loops.
Comment: 14 pages, 1 figure, uses natbib.sty, latexcad.sty; submitted to the Bulletin of the Academy of Sciences of M
Comment: 14 pages, 1 figure, uses natbib.sty, latexcad.sty; submitted to the Bulletin of the Academy of Sciences of M
Externí odkaz:
http://arxiv.org/abs/math/0506085