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A remark on closed noncommutative subspaces

Author: E. S. Letzter
Journal: Proc. Amer. Math. Soc. 135 (2007), 1-4
MSC (2000): Primary 18E15; Secondary 14A22
Published electronically: August 16, 2006
MathSciNet review: 2280167
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Abstract: Given an abelian category with arbitrary products, arbitrary coproducts, and a generator, we show that the closed subspaces (in the sense of A. L. Rosenberg) are parameterized by a suitably defined poset of ideals in the generator. In particular, the collection of closed subspaces is itself a small poset.

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E. S. Letzter
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Received by editor(s): May 25, 2005
Received by editor(s) in revised form: July 19, 2005
Published electronically: August 16, 2006
Additional Notes: The author thanks the Department of Mathematics at the University of Pennsylvania for its hospitality; the research for this paper was undertaken while he was a visitor on sabbatical there. The author is grateful for support during this period from a Temple University Research and Study Leave Grant. This research was also supported in part by a grant from the National Security Agency.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.