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Articolul urmator |
257 1 |
Ultima descărcare din IBN: 2023-07-07 12:26 |
Căutarea după subiecte similare conform CZU |
512.548.72 (2) |
Algebră (410) |
SM ISO690:2012 SYRBU, Parascovia, KUZNETSOVA, Elena. On recursively differentiable k-quasigroups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2022, nr. 2(99), pp. 68-75. ISSN 1024-7696. DOI: https://doi.org/10.56415/basm.y2022.i2.p68 |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 2(99) / 2022 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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DOI:https://doi.org/10.56415/basm.y2022.i2.p68 | ||||||
CZU: 512.548.72 | ||||||
MSC 2010: 20N05, 20N15, 11T71. | ||||||
Pag. 68-75 | ||||||
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Rezumat | ||||||
Recursive differentiability of linear k-quasigroups (k 2) is studied in the present work. A k-quasigroup is recursively r-differentiable (r is a natural number) if its recursive derivatives of order up to r are quasigroup operations. We give necessary and sufficient conditions of recursive 1-differentiability (respectively, r-differentiability) of the k-group (Q,B), where B(x1, ..., xk) = x1 · x2 · ... · xk, 8x1, x2, ..., xk 2 Q, and (Q, ·) is a finite binary group (respectively, a finite abelian binary group). The second result is a generalization of a known criterion of recursive r-differentiability of finite binary abelian groups [4]. Also we consider a method of construction of recursively r-differentiable finite binary quasigroups of high order r. The maximum known values of the parameter r for binary quasigroups of order up to 200 are presented. |
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Cuvinte-cheie k-ary quasigroup, recursive derivative, Recursively differentiable quasigroup |
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