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ON CONJUGATE PRIME IDEALS OF TENSOR PRODUCTS OF k-ALGEBRAS.
- Source :
- Journal of Algebra & Its Applications; Feb2010, Vol. 9 Issue 1, p1-10, 10p
- Publication Year :
- 2010
-
Abstract
- The purpose of this paper is to explore new aspects of the prime ideal structure of tensor products of algebras over a field k. We prove that given a k-algebra A and a normal field extension K of k (in the sense of Galois theory), then for any prime ideals P<subscript>1</subscript> and P<subscript>2</subscript> of K ⊗<subscript>k</subscript> A lying over a fixed prime ideal p of A, there exists a k-automorphism σ of K such that (σ ⊗<subscript>k</subscript>id<subscript>A</subscript>)(P<subscript>1</subscript>) = P<subscript>2</subscript>. As an Application, we establish a result related to the dimension theory of tensor products stating that, for two arbitrary k-algebras A and B, the minimal prime ideals of p ⊗<subscript>k</subscript> B + Aσ<subscript>k</subscript> q have the same height, for any prime ideals p and q of A and B, respectively. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 9
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 48282677
- Full Text :
- https://doi.org/10.1142/S0219498810003720