论文标题
Malcolmson Semigroups
Malcolmson semigroups
论文作者
论文摘要
受到C*-Algebra的Cuntz Semigroup的构建的启发，我们介绍了Malcolmson Semigroup的基质和有限呈现的模块Malcolmson Semigroup，用于Unital环。这两个半群显示通常具有同构Grothendieck组，并且对von Neumann常规环是同构。对于Unital c*-Algebras，表明矩阵Malcolmson Semigroup对Cuntz Semigroup具有自然的量规订单保存同构，每个尺寸函数都是Sylvester矩阵级别函数，并且存在Sylvester Matrix级别级别函数，不是尺寸函数。
Inspired by the construction of the Cuntz semigroup for a C*-algebra, we introduce the matrix Malcolmson semigroup and the finitely presented module Malcolmson semigroup for a unital ring. These two semigroups are shown to have isomorphic Grothendieck group in general and be isomorphic for von Neumann regular rings. For unital C*-algebras, it is shown that the matrix Malcolmson semigroup has a natural surjective order-preserving homomorphism to the Cuntz semigroup, every dimension function is a Sylvester matrix rank function, and there exist Sylvester matrix rank functions which are not dimension functions.
