Advances In Algebra And Combinatorics: Proceedings of the by K. P. Shum, E. Zelmanov, Jiping Zhang, Li Shangzhi PDF

By K. P. Shum, E. Zelmanov, Jiping Zhang, Li Shangzhi

ISBN-10: 9812790004

ISBN-13: 9789812790002

This quantity is a compilation of lectures on algebras and combinatorics provided on the moment foreign Congress in Algebra and Combinatorics. It stories on not just new effects, but additionally on open difficulties within the box. The complaints quantity turns out to be useful for graduate scholars and researchers in algebras and combinatorics. The individuals contain eminent figures akin to E Bannai, P Hilton, M Jambu, I Kotsireas, B Schein and A Smoktunowicz.

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Example text

It is obvious that > is a monomial order on N . Such an order is also called the deg-lex order on N = X * Y * . Let f and g be monic polynomials of k N and w = w x w y E N . Then we have found 16 types of compositions of inclusion and intersection. S is called a Grobner-Shirshov basis in kN = k ( X ) 8 k ( Y ) if all compositions of elements in S are trivial modulo S. 5. Let S k ( X )8 k ( Y ) with each s E S monic and “ < ” the deg-lea: order o n N = X * Y * as before. Then the following statements are equivalent: (1) S is a Grobner-Shirshov basis in k ( X ) 8 k ( Y ) .

2. ([24]) Let 3 be obtained f r o m a generic quantum polynomial algebra 0, and f E 3 \ k. Then the centralizer C ( f ) of f in 3 is commutative and is a maximal subfield in 3. 3 (K. Goodearl, private communication). Let X be a subfield in F (at is not necessarily assumed that 0, is a generic quan- tum polynomial algebra). Then the transcendent degree of K over k does n o exceed Km11 dimension of l c ~ [ X ?. ~ . ,,X;']. If r = n the Krull and global dimensions of 0, are equal to the maximal number of commuting monomials whose multi-indices are independent in Z n [12].

Goodearl, private communication). Let X be a subfield in F (at is not necessarily assumed that 0, is a generic quan- tum polynomial algebra). Then the transcendent degree of K over k does n o exceed Km11 dimension of l c ~ [ X ?. ~ . ,,X;']. If r = n the Krull and global dimensions of 0, are equal to the maximal number of commuting monomials whose multi-indices are independent in Z n [12]. 4 (Zelenova S . ) . Let K be a commutative subalgebra of the algebra 0, which is not supposed to be generic.

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Advances In Algebra And Combinatorics: Proceedings of the Second International Congress in Algebra and Cominatorics Guangzhou, China 2 - 4 July 2007; Beijing, China 6 - 11 July 2007; Xian, by K. P. Shum, E. Zelmanov, Jiping Zhang, Li Shangzhi


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