AN ANALOGUE OF HILBERT%26apos;S SYZYGY THEOREM FOR THE ALGEBRA OF ONE-SIDED INVERSES OF A POLYNOMIAL ALGEBRA

作者：Bavula V V^*

来源：Proceedings of the American Mathematical Society, 2012, 140(10): 3323-3331.

• The algebras of one-sided inverses
• the algebra of one-sided inverses of a polynomial algebra
• the global dimension
• Hilbert%26apos
• s Syzygy Theorem
• the projective dimension
• the weak dimension

An analogue of Hilbert%26apos;s Syzygy Theorem is proved for the algebra S-n(A) of one-sided inverses of the polynomial algebra A[x(1) , . . . , x(n)] over an arbitrary ring A: %26lt;br%26gt;l.gldim(S-n(A)) = l.gldim(A) + n. %26lt;br%26gt;The algebra S-n(A) is noncommutative, neither left nor right Noetherian and not a domain. The proof is based on a generalization of the Theorem of Kaplansky (on the projective dimension) obtained in the paper. As a consequence it is proved that for a left or right Noetherian algebra A: %26lt;br%26gt;w.dim(S-n(A)) = w.dim(A) + n.

• 出版日期2012-10