Lattices of two-sided ideals of locally matricial algebras and the Γ-invariant problem
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We develop a method of representation of distributive (V,0,1)-semilattices as semilattices of finitely generated ideals of locally matricial algebras. We use the method to reprove two representation results by G. M. Bergman and prove a new one that every distributive (0,1)-lattice is, as a semilattice, isomorphic to the semilattice of all finitely generated ideals of a locally matricial algebra. We apply this fact to solve the Γ-invariant problem.
KeywordsDistributive Lattice Ideal Lattice Direct System Dense Lattice Compact Element
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- [Be] G. M. Bergman,Von Neumann regular rings with tailor-made ideal lattices, unpublished notes (1986).Google Scholar
- [T1] J. Trlifaj,Modules over non-perfect rings, inAdvances in Algebra and Model Theory, Gordon and Breach, Philadelphia, 1996, pp. 471–492.Google Scholar
- [T2] J. TrlifajUniform modules, Γ-invariants, and Ziegler spectra for regular rings, Proc. ICAGM’98 Birkhäuser Verlag, Basel, 1999, pp. 327–340.Google Scholar