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![]() URSU, Leonid. Definition and example of n-ary Moufang loop. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, pp. 107-108. ISBN 978-9975-76-247-2. |
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Conference on Applied and Industrial Mathematics Ediţia a 26-a, 2018 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, România, Romania, 20-22 septembrie 2018 | ||||||
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Pag. 107-108 | ||||||
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Rezumat | ||||||
In this work necessary and sucient conditions that isotope of n-IP-loop (n 2 N, n > 3) is also n-IP-loop are proved. De nition of n-ary Moufang loop is given, example of such loop is constructed. Keywords: n-IP-quasigroup, n-IP-loop, Moufang loop, isotopy, LP-isotopy. Main concepts and de nitions. Quasigroup Q(A) of arity n, n 2, is called an n-IPquasigroup if there exist permutations ij ; i; j 2 1; n of the set Q such that the following identities are true: A(fijxjgi-1 j=1;A(xn1 ); fijxjgnj =i+1) = xi for all xn1 2 Qn, where ii = i n+1 = ", " denotes identity permutation of the set Q [1]. The matrix ij = 2 664 " 12 13 : : : 1n " 21 " 23 : : : 2n " : : : : : : : : : : : : : : : : : : : : : : : : : : : 31 32 " : : : " " 3 775 is called an inversion matrix for an n-IP-quasigroup, the permutations i;j are called inversion permutations. An element e is called a unit of n-ary operation Q(), if the following equality is true ( i-1 e ; x; n-i e ) = x for all x 2 Q and i 2 1; n. n-Ary quasigroup with unit element is called an n-ary loop [1]. |
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