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An affine oriented matroid is a combinatorial abstraction of an affinehyperplane arrangement. From it, Novik, Postnikov and Sturmfels constructed asquarefree monomial ideal in a polynomial ring, called an oriented matroidideal, and got beautiful results. Developing their theory, we will show thefollowing.  (1) If an oriented matroid ideal is Cohen-Macaulay, then the bounded complex(a regular CW complex associated with it) of the corresponding affine orientedmatroid is a contractible homology manifold with boundary. This is closelyrelated to Dong's theorem, which used to be "Zaslavsky's conjecture".  (2) We characterize the affine oriented matroid whose corresponding ideal isCohen-Macaulay.  (3) In the Cohen-Macaulay case, we give a description of the canonical moduleof the residue class ring by an oriented matroid ideal.

The Cohen-Macaulayness of the bounded complex of an affine oriented matroid