The algebra of one-sided inverses of a polynomial algebra

作者：Bavula V V^*

来源：Journal of Pure and Applied Algebra, 2010, 214(10): 1874-1897.

DOI：10.1016/j.jpaa.2009.12.033

We study in detail the algebra S(n) in the title which is an algebra obtained from a polynomial algebra P(n) in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of P(n). The algebra S(n) is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is proved that the classical Krull dimension of S(n) is 2n; but the weak and the global dimensions of S(n) are n. The prime and maximal spectra of S(n) are found, and the simple S(n)-modules are classified. It is proved that the algebra S(n) is central, prime, and catenary. The set II(n) of idempotent ideals of S(n) is found explicitly. The set II(n) is a finite distributive lattice and the number of elements in the set II(n) is equal to the Dedekind number sigma(n).

• 出版日期2010-10