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Displaying similar documents to “Free Bicommutative Algebras”

Universal Enveloping Algebras of Nonassociative Structures

Tvalavadze, Marina (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99. This is a survey paper to summarize the latest results on the universal enveloping algebras of Malcev algebras, triple systems and Leibniz n-ary algebras.

q-Leibniz Algebras

Dzhumadil'daev, A. S. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25. An algebra (A,ο) is called Leibniz if aο(bοc) = (a ο b)ο c-(a ο c) ο b for all a,b,c ∈ A. We study identities for the algebras A(q) = (A,οq), where a οq b = a ο b+q b ο a is the q-commutator. Let Char K ≠ 2,3. We show that the class of q-Leibniz algebras is defined by one identity of degree 3 if q2 ≠ 1, q ≠−2, by two identities of degree 3 if q = −2, and by the commutativity identity and one identity...

Free Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo, Nora Oliva, Alicia Ziliani (2018)

Bulletin of the Section of Logic

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Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1 (2014), pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ(∼x)* = (∼(xΛ(∼x)*))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new...

A review on δ-structurable algebras

Noriaki Kamiya, Daniel Mondoc, Susumu Okubo (2011)

Banach Center Publications

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In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.

The class of 2-dimensional neat reducts is not elementary

Tarek Sayed Ahmed (2002)

Fundamenta Mathematicae

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SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends...