Relations between n-ary and binary comodules

Zekovich Biljana

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661

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2017-03-17 15:09

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512.5/.6 (2)

Algebra (410)

SM ISO690:2012

ZEKOVICH, Biljana. Relations between n-ary and binary comodules. In: Quasigroups and Related Systems, 2015, vol. 23, nr. 2(34), pp. 325-332. ISSN 1561-2848.

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Quasigroups and Related Systems

Volumul 23, Numărul 2(34) / 2015 / ISSN 1561-2848

Relations between n-ary and binary comodules

CZU: 512.5/.6

Pag. 325-332

Zekovich Biljana

University of Montenegro Podgorica

Disponibil în IBN: 6 mai 2016

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We construct a binary algebra R = C(n_1)/I for an n-ary algebra C and prove that M is an n-ary left C-module if and only if M is a binary left R-module. In the dual case, for an n-ary coalgebra C, we construct a binary coalgebra: C_(n_1) = n\_2 j=1 Ker h _ 1(n_2) C _ 1j C _ 1(n_2_j) C i _ C(n_1) and prove that M is an n-ary right C-comodule if and only if M is a binary right C_(n_1)comodule. In the end, we prove that for n-ary _nite generated coalgebra C over a _eld k, C_(n_1) is the binary coalgebra, on the other hand, C_ is an n-ary algebra, for which, we construct the binary algebra R = (C_)(n_1)/I . If C is a _nite-dimensional n-ary coalgebra over a _eld k, then C_ is a n-ary algebra and (C_(n_1))_ _= (C_)(n_1) _ I: Dually, if C is an n-ary _nite generated algebra over a _eld k, then R = C(n_1) _ I is a binary algebra and C_ is an n-ary coalgebra. Moreover, (C_)_(n_1) _= _ C(n_1) _ I .

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