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1.
Partial abelian monoids (PAMs) are structures (), where is a partially defined binary operation with domain , which is commutative and associative in a restricted sense, and 0 is the neutral element. PAMs with the Riesz decomposition
properties and binary relations with special properties on PAMs are studied. Relations with abelian groups, dimension equivalence
and K
0 for AF C*-algebras are discussed.
Received September 17, 2000; accepted in final form March 13, 2002. 相似文献
2.
Representations of distributive semilattices in ideal lattices of various algebraic structures 总被引:2,自引:0,他引:2
We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000. 相似文献