Semigroup operations which are distributive over a given semigroup operation on positive real numbers

Oka Hirokazu and Miura Takeshi and Takahasi Sin-Ei: Semigroup operations which are distributive over a given semigroup operation on positive real numbers. In: Acta scientiarum mathematicarum, (86) 3-4. pp. 493-502. (2020)

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Abstract

Let R+ be the space of positive real numbers with the ordinary topology and let ⋆ be an arbitrary cancellative continuous semigroup operation on R+ or some special noncancellative continuous semigroup operation on R+. We characterize the set D −1 ⋆ (R+) of all cancellative continuous semigroup operations on R+ which are distributive over ⋆ in terms of homeomorphism. As a consequence, it is shown that if ⋆ is homeomorphically isomorphic to the ordinary addition + on R+, any element of D −1 ⋆ (R+) is homeomorphically isomorphic to the ordinary multiplication on R+, and that if ⋆ is cancellative and not homeomorphically isomorphic to +, then D −1 ⋆ (R+) is empty. Moreover, if ⋆ is homeomorphically isomorphic to some special noncancellative continuous semigroup operation on R+, D −1 ⋆ (R+) is also shown to be empty.

Item Type:	Article
Heading title:	Analysis
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2020
Volume:	86
Number:	3-4
ISSN:	2064-8316
Page Range:	pp. 493-502
Language:	English
Related URLs:	http://acta.bibl.u-szeged.hu/73790/
DOI:	10.14232/actasm-020-116-1
Uncontrolled Keywords:	Matematika
Additional Information:	Bibliogr.: p. 501-502. ; összefoglalás angol nyelven
Date Deposited:	2021. Nov. 15. 13:33
Last Modified:	2021. Nov. 15. 13:33
URI:	http://acta.bibl.u-szeged.hu/id/eprint/73900

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