Results 221 to 230 of about 1,101 (266)
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Fuzzy Sets and Systems, 2014
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Pan, Fang-Fang, Han, Sheng-Wei
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Pan, Fang-Fang, Han, Sheng-Wei
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International Journal of Algebra and Computation, 2000
A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L.
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A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L.
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Algebra and Logic, 1988
This work is based on the results and methods of the author's earlier study of Jordan \(A\)-algebras [Algebra Logika 26, No. 6, 731--755 (1987; Zbl 0648.17008)]. The term algebra is used when working over a commutative associative ring with \(1/2\), while the term ring is used when working over the integers.
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This work is based on the results and methods of the author's earlier study of Jordan \(A\)-algebras [Algebra Logika 26, No. 6, 731--755 (1987; Zbl 0648.17008)]. The term algebra is used when working over a commutative associative ring with \(1/2\), while the term ring is used when working over the integers.
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Canadian Journal of Mathematics, 1968
By a PQ (product-quotients) algebra, we mean a non-empty set together with three single-valued and not necessarily associative operations ., / , \ that we shall treat as product, right quotient, and left quotient although we require no relation between them. The theory of binary systems provides the following examples:A.
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By a PQ (product-quotients) algebra, we mean a non-empty set together with three single-valued and not necessarily associative operations ., / , \ that we shall treat as product, right quotient, and left quotient although we require no relation between them. The theory of binary systems provides the following examples:A.
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Canadian Journal of Mathematics, 1985
For us an “algebra” is a finitary “universal algebra” in the sense of G. Birkhoff [9]. We are concerned in this paper with algebras whose endomorphisms are determined by small subsets. For example, an algebra A is rigid (in the strong sense) if the only endomorphism on A is the identity idA. In this case, the empty set determines the endomorphism set E(
Bankston, Paul, Schutt, Richard
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For us an “algebra” is a finitary “universal algebra” in the sense of G. Birkhoff [9]. We are concerned in this paper with algebras whose endomorphisms are determined by small subsets. For example, an algebra A is rigid (in the strong sense) if the only endomorphism on A is the identity idA. In this case, the empty set determines the endomorphism set E(
Bankston, Paul, Schutt, Richard
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Mathematics of the USSR-Sbornik, 1973
The class of all compact topological algebras in any variety of universal algebras is closed under the operations of taking direct products, closed sub-algebras and factor-algebras. This fact allows of a beginning to a theory of free compact algebras modelled on well-known studies of free topological groups and algebras by A. A. Markov, M. I. Graev and
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The class of all compact topological algebras in any variety of universal algebras is closed under the operations of taking direct products, closed sub-algebras and factor-algebras. This fact allows of a beginning to a theory of free compact algebras modelled on well-known studies of free topological groups and algebras by A. A. Markov, M. I. Graev and
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Free factor algebras of free linear ?-algebras
Mathematical Notes of the Academy of Sciences of the USSR, 1972This paper concerns free linear Ω-algebras in certain varieties and their subalgebras and factor algebras. Conditions are given ensuring that an epimorphic image of a free linear Ω-algebra in a variety given by permutation identities of zero order is free in this variety. An example is constructed of a variety of linear algebras in which this assertion
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On Polynomial Algebras and Free Algebras
Canadian Journal of Mathematics, 1968It is well known that given the polynomial algebra (for definitions, see §2), an algebra of type τ, and a sequence a of elements of , one can define a congruence relation θa of such that the factor algebra is isomorphic to the subalgebra of generated by a, and the isomorphism is given in a very simple way.
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Free brace algebras are free prelie algebras
2008Let g be a free brace algebra. This structure implies that g is also a prelie algebra and a Lie algebra. It is already known that g is a free Lie algebra. We prove here that g is also a free prelie algebra, using a description of g with the help of planar rooted trees, a permutative product, and anipulations on the Poincar -Hilbert series of g.
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Czechoslovak Mathematical Journal, 2003
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