Abstract.
In this paper we demonstrate that every positive totally ordered commutative monoid on 2 generators satisfying a weak cancellation property is a convex Rees quotient of a sub-monoid of a totally ordered Abelian group. In [1], the current author, along with Evans, Konikoff, Mathis, and Madden, employed the work of Hion, [5], to demonstrate that the monoid ring of all finite formal sums over a totally ordered domain is a formally real totally ordered ring providing the totally ordered monoid satisfies this weak cancellation property and is a convex Rees quotient of a sub-monoid of a totally ordered Abelian group. Therefore, we provide here significant information about a condition for the construction of formally real totally ordered monoid algebras.
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Received November 4, 2003; accepted in final form November 18, 2004.
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Whipple, G.W. A condition for constructing formally real monoid algebras. Algebra univers. 54, 53–63 (2005). https://doi.org/10.1007/s00012-005-1921-5
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DOI: https://doi.org/10.1007/s00012-005-1921-5