The associativity equation revisited

R. Craigen, Z. Páles

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

Consideration of the Associativity Equation, x {ring operator} (y {ring operator} z) = (x {ring operator} y) {ring operator} z, in the case where {ring operator}:I × I → I (I a real interval) is continuous and satisfies a cancellation property on both sides, provides a complete characterization of real continuous cancellation semigroups, namely that they are topologically order-isomorphic to addition on some real interval: ( - ∞, b), ( - ∞, b], -∞, +∞), (a, + ∞), or [a, + ∞) - where b = 0 or -1 and a = 0 or 1. The original proof, however, involves some awkward handling of cases and has defied streamlining for some time. A new proof is given following a simpler approach, devised by Páles and fine-tuned by Craigen.

Original languageEnglish
Pages (from-to)306-312
Number of pages7
JournalAequationes Mathematicae
Volume37
Issue number2-3
DOIs
Publication statusPublished - Jun 1989

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Associativity
Ring
Operator
Cancellation
Interval
Semigroup
Isomorphic

Keywords

  • AMS (1980) subject classification: Primary 39B40, Secondary 22A05, 06F05

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The associativity equation revisited. / Craigen, R.; Páles, Z.

In: Aequationes Mathematicae, Vol. 37, No. 2-3, 06.1989, p. 306-312.

Research output: Contribution to journalArticle

Craigen, R. ; Páles, Z. / The associativity equation revisited. In: Aequationes Mathematicae. 1989 ; Vol. 37, No. 2-3. pp. 306-312.
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