Results 291 to 300 of about 233,188 (306)
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Varieties of algebras and algebraic varieties
Israel Journal of Mathematics, 1996The paper contains a brief account of ideas and results, which are described in [1] and [2] with details and proofs. The subject of the paper is algebraic geometry in arbitrary algebraic structures.
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Connections on algebraic varieties [PDF]
, 2020 Most of this book deals with differential systems in a geometric context, in several variables. In order to give such systems an intrinsic meaning, two languages are at disposal, which are in principle equivalent: integrable connections and D-modules.
Andre Y., Baldassarri F., Cailotto M.
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Arithmetic on algebraic varieties
The Annals of Mathematics, 1951D. G. Northcott has recently contributed some interesting new theorems ([4a], [4b]) to a subject which I introduced in my thesis [1] under the above-given title, and which had been further developed by Siegel [2] and myself [3]. It is my purpose here, by making explicit some concepts which had remained implicit in these papers, to supply what seems to ...
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2015
We at last formally define the concept of a (set-based) algebra, consider classes of algebras defined by families of identities (varieties), and prove Birkhoff’s HSP theorem. We devote several pages to Lie algebras. Clonal categories, and Lawvere’s Structure and Semantics functors, are briefly introduced.
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We at last formally define the concept of a (set-based) algebra, consider classes of algebras defined by families of identities (varieties), and prove Birkhoff’s HSP theorem. We devote several pages to Lie algebras. Clonal categories, and Lawvere’s Structure and Semantics functors, are briefly introduced.
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Algebraic varieties in the symmetric algebra
Linear and Multilinear Algebra, 1986We describe a procedure for constructing a broad class of projective algebraic varieties in the various summands of the symmetric algebraS( V), where V is a finite dimensional vector space whose underlying scalar field is algebraically closed and of characteristic zero.
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1982
This final chapter returns to the general theory of algebras over a field. It provides a brief introduction to the theory of polynomial identities for algebras. Our main goal is to prove Amitsur’s Theorem which establishes the existence of finite dimensional central simple division algebras that are not crossed products.
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This final chapter returns to the general theory of algebras over a field. It provides a brief introduction to the theory of polynomial identities for algebras. Our main goal is to prove Amitsur’s Theorem which establishes the existence of finite dimensional central simple division algebras that are not crossed products.
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1993
A non-empty set A is called a universal algebra with a set of operations, Ω if for any ω ∈ Ω there exists a natural number n = n(ω) (it is possible that n = 0) such that ω is an n-ary (or n-local) operation on A, i.e. ω is a mapping from \( {A^n} = \underbrace {A \times \ldots \times A}_n \) into A.
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A non-empty set A is called a universal algebra with a set of operations, Ω if for any ω ∈ Ω there exists a natural number n = n(ω) (it is possible that n = 0) such that ω is an n-ary (or n-local) operation on A, i.e. ω is a mapping from \( {A^n} = \underbrace {A \times \ldots \times A}_n \) into A.
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Journal of Applied Non-Classical Logics, 1999
ABSTRACT We characterize, for every subvariety V of the variety of all MV- algebras, the free objects in V. We use our results to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.
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ABSTRACT We characterize, for every subvariety V of the variety of all MV- algebras, the free objects in V. We use our results to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.
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