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1978•Proceedings of the American Mathematical SocietyOpen access

Positive derivations on partially ordered linear algebra with an order unit

Taen Yu Dai, Ralph DeMarr

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Abstract

We show that the range of a positive derivation on a Dedekind σ \sigma -complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.

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We show that the range of a positive derivation on a Dedekind σ \sigma -complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.

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Available abstract

We show that the range of a positive derivation on a Dedekind σ \sigma -complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.

Key concepts: Unit (ring theory), Algebra over a field, Dedekind cut, Mathematics, Order (exchange), Semantics (computer science), Set (abstract data type), Annotation

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