Clean unital $\ell$-groups

Rok, strany: 2013, 979 - 992

A ring with identity is said to be clean if every element can be written as a sum of a unit and an idempotent. The study of clean rings has been at the forefront of ring theory over the past decade. The theory of partially-ordered groups has a nice and long history and since there are several ways of relating a ring to a (unital) partially-ordered group it became apparent that there ought to be a notion of a clean partially-ordered group. In this article we define a clean unital lattice-ordered group; we state and prove a theorem which characterizes clean unital $\ell$-groups. We mention the relationship of clean unital $\ell$-groups to algebraic $K$-theory. In the last section of the article we generalize the notion of clean to the non-unital context and investigate this concept within the framework of $\mathbf{W}$-objects, that is, archimedean $\ell$-groups with distinguished weak order unit.

ISO 690:

Hager, A., Kimber, C., Mcgovern, W. 2013. Clean unital $\ell$-groups. In Mathematica Slovaca, vol. 63, no.5, pp. 979-992. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0148-8

APA:

Hager, A., Kimber, C., Mcgovern, W. (2013). Clean unital $\ell$-groups. Mathematica Slovaca, 63(5), 979-992. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0148-8