Results 1  10
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13
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 Proceedings of the International Conference on Mathematical Logic, Algebra and Set Theory, dedicated to 100 anniversary of P.S.Novikov, Proceedings MIAN
, 2002
"... Abstract. Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of g ..."
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Cited by 18 (3 self)
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Abstract. Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in Θ and of geometric relations between them. The main problem considered in the paper is when different H1 and H2 have the same geometry.
E.Plotkin, Automorphisms of the category of free algebras of varieties, Electron
 Res. Announs. Amer. Math. Soc
"... ..."
The group of automorphisms of the category of free associative algebras
"... In this paper, the problem formulated in [8] is solved. We prove, that the group of automorphisms of the category of free associative algebras is generated by semiinner and mirror automorphisms. 1 ..."
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Cited by 6 (2 self)
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In this paper, the problem formulated in [8] is solved. We prove, that the group of automorphisms of the category of free associative algebras is generated by semiinner and mirror automorphisms. 1
ISOTYPED ALGEBRAS
, 812
"... Abstract. The paper is essentially a continuation of [PZ], whose main notion is that of logicgeometrical equivalence of algebras (LGequivalence of algebras). This equivalence of algebras is stronger than elementary equivalence. In the paper we introduce the notion of isotyped algebras and relate i ..."
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Abstract. The paper is essentially a continuation of [PZ], whose main notion is that of logicgeometrical equivalence of algebras (LGequivalence of algebras). This equivalence of algebras is stronger than elementary equivalence. In the paper we introduce the notion of isotyped algebras and relate it to LGequivalence. We show that these notions coincide. The idea of the type is one of the central ideas in Model Theory. The correspondence introduced in the paper stimulates a bunch of problems which connect universal algebraic geometry and Model Theory. We provide a new general view on the subject, arising ”on the territory ” of universal algebraic geometry. This insight yields also applications of algebraic logic in Model Theory. Application of algebraic logic in Model theory makes some approaches more transparent. CONTENT
unknown title
, 2008
"... The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence. ..."
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The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence.
Hebrew University
, 2002
"... We prove that every automorphism of the category of free Lie algebras is a semiinner automorphism. This solves the problem 3.9 from [19] for Lie algebras. ..."
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We prove that every automorphism of the category of free Lie algebras is a semiinner automorphism. This solves the problem 3.9 from [19] for Lie algebras.
ACTION TYPE GEOMETRICAL EQUIVALENCE OF REPRESENTATIONS OF GROUPS.
, 2008
"... In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over KF2, where F2 is a free group with 2 generators (compare with [Ca] where a continuum of non isomorphic simple 2generated groups is constructed). Using this fact we give an example of a non action ..."
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In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over KF2, where F2 is a free group with 2 generators (compare with [Ca] where a continuum of non isomorphic simple 2generated groups is constructed). Using this fact we give an example of a non action type logically Noetherian representation (Section 9). In general, the topic of this paper is the action type algebraic geometry of representations of groups. For every variety of algebras Θ 1 and every algebra H ∈ Θ we can consider an algebraic geometry in Θ over H. Algebras in Θ may be many sorted (not necessarily one sorted) algebras. A set of sorts Γ is fixed for each Θ. This theory can be applied to the variety of representations of groups over fixed commutative ring K with unit. We consider a representation as two sorted algebra (V,G), where V is a Kmodule, and G is a group acting on
The group of automorphisms of semigroup End(P[X])
, 2004
"... In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semiinner automorphisms. 1 ..."
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In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semiinner automorphisms. 1