N ov 2 00 3 HOMOLOGICAL DIMENSION OF CROSSED PRODUCTS ∗
نویسنده
چکیده
Throughout this paper, k is a field, R is an algebra over k, and H is a Hopf algebra over k. We say that R# σ H is the crossed product of R and H if R# σ H becomes an algebra over k by multiplication: (a#h)(b#g) = h,g a(h 1 · b)σ(h 2 , g 1)#h 3 g 2 Let lpd(R M), lid(R M) and lf d(R M) denote the left projective dimension, left injective dimension and left flat dimension of left R-module M, respectively. Let lgD(R) and wD(R) denote the left global dimension and weak dimension of algebra R, respectively. Crossed products are very important algebraic structures. The relation between homological dimensions of algebra R and crossed product R# σ H is often studied.
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