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165,803
Groebner Bases In NonCommutative Algebras
 In Proc.oftheInternational Symposium on Symbolic and Algebraic Computation (ISSAC’88
, 1989
"... INTRODUCTION Recently, the use of Groebner bases and Buchberger algorithm [BUC1,2,4] has been generalised from the case of commutative polynomials to finitely generated algebras R over a field k, R = k<Xl,...,Xn>, s.t. for each i < j, for some cij ( k, for some commutative polynomial Pij ..."
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polynomial rings can be described as follows: impose on the noncommutative polynomial ring k<X 1 ,...,Xn> a graduation on N n,
RESTRICTIONS OF NONCOMMUTATIVE ALGEBRAS WHICH INDUCE COMMUTATIVITY
"... Abstract. The nontrivial Clifford algebras over the ring Z are noncommutative. On the other hand, the Clifford algebras over the ring Z2 are commutative. This result is nontrivial in that it does not depend solely on either Z2 or the Clifford algebras. The nontrivial Clifford algebras over the ..."
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Abstract. The nontrivial Clifford algebras over the ring Z are noncommutative. On the other hand, the Clifford algebras over the ring Z2 are commutative. This result is nontrivial in that it does not depend solely on either Z2 or the Clifford algebras. The nontrivial Clifford algebras over the
NONCOMMUTATIVE ALGEBRAIC GEOMETRY AND THE STUDY OF NONCOMMUTATIVE TORI
, 2008
"... I would like to thank all the organizers of the International Workshop on Noncommutative Geometry, 2005 for giving me this opportunity to speak. In section 1 we shall browse through some interesting definitions and constructions which will be referred to later on. In section 2 we shall deal with non ..."
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I would like to thank all the organizers of the International Workshop on Noncommutative Geometry, 2005 for giving me this opportunity to speak. In section 1 we shall browse through some interesting definitions and constructions which will be referred to later on. In section 2 we shall deal
Resolution of stringy singularities by noncommutative algebras
 JHEP 0106
"... Preprint typeset in JHEP style. PAPER VERSION ..."
On Preimages of Ideals in Certain Non–commutative Algebras
"... Abstract. In this paper we present new algorithms for non–commutative Gröbner ready algebras, which enable one to perform advanced operations with ideals and modules. In spite of the big interest in algorithmic treatment of related problems, preimage of ideal and central character decomposition we ..."
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Abstract. In this paper we present new algorithms for non–commutative Gröbner ready algebras, which enable one to perform advanced operations with ideals and modules. In spite of the big interest in algorithmic treatment of related problems, preimage of ideal and central character decomposition
On Linear Equations in Some NonCommutative Algebras
, 1999
"... The problem of solving linear equations in a... In this paper we will demonstrate a method by which it is possible to find all the solutions to linear equations in certain factor algebras of the noncommutative polynomial ring. The commutative case reduces to computing syzygy modules, which is treate ..."
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is treated in Adams [1]. Here we will consider algebras the center of which is sufficiently large, in the sense that the former can be considered a Noetherian module over a subalgebra of its center. We will show that with the aid of Gröbner basis technique, the problem of finding the solutions in the noncommutative
PARTIAL DESINGULARIZATIONS ARISING FROM NONCOMMUTATIVE ALGEBRAS
, 2005
"... Let X be a singular affine normal variety with coordinate ring R and assume that there is an Rorder Λ admitting a stability structure θ such that the scheme of θsemistable representations is smooth, then we construct a partial desingularization of X with classifiable remaining singularities. In d ..."
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Let X be a singular affine normal variety with coordinate ring R and assume that there is an Rorder Λ admitting a stability structure θ such that the scheme of θsemistable representations is smooth, then we construct a partial desingularization of X with classifiable remaining singularities. In dimension 3 this explains the omnipresence of conifold singularities in partial desingularizations of quotient singularities. In higher dimensions we have a small list of singularity types generalizing the role of the conifold singularity.
ON SOME APPROACHES TOWARDS NONCOMMUTATIVE ALGEBRAIC GEOMETRY
"... The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas com ..."
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The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas
A BRIEF SURVEY OF NONCOMMUTATIVE ALGEBRAIC GEOMETRY
"... The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas com ..."
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The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas
LINEAR FREE RESOLUTIONS OVER NONCOMMUTATIVE ALGEBRAS
, 2003
"... Abstract. The main result of this paper is that over a noncommutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions. Eisenbud and Goto, Avramov and Eisenbud, and this author have all studied whether high truncations of finitely generated graded mo ..."
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Abstract. The main result of this paper is that over a noncommutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions. Eisenbud and Goto, Avramov and Eisenbud, and this author have all studied whether high truncations of finitely generated graded
Results 1  10
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165,803