On simple and semisimple quantales

KRUML, David and Jan PASEKA. On simple and semisimple quantales. In Topology Atlas Invited Contributions. Toronto: Topology Atlas, 2002, p. 1-13. ISSN 1703-0048.

Basic information

Original name

On simple and semisimple quantales

Authors

KRUML, David (203 Czech Republic, guarantor) and Jan PASEKA (203 Czech Republic)

Edition

Toronto, Topology Atlas Invited Contributions, p. 1-13, 2002

Publisher

Topology Atlas

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Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10101 Pure mathematics

Country of publisher

Canada

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

RIV identification code

RIV/00216224:14310/02:00006486

Organization unit

Faculty of Science

ISSN

Keywords in English

simple quantale; semisimple quantale

Tags

semisimple quantale, Simple quantale

Tags

International impact, Reviewed

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Abstract

V originále

In a recent paper, J. W. Pelletier and J. Rosicky published a characterization of *-simple *-quantales. Their results were adapted for the case of simple quantales by J Paseka. In this paper we present similar characterizations which do not use a notion of discrete quantale. We also show a completely new characterization based on separating and cyclic sets. Further we explain a link to simple quantale modules. To apply these characterizations, we study (*-)semisimple (*-)quantales and discuss some other perspectives. Our approach has connections with several earlier works on the subject.

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Links

GA201/99/0310, research and development project	Name: Kategoriální metody teorie struktur a informatiky Investor: Czech Science Foundation, Categorical methods of the theory of structures and computer science
MSM 143100009, plan (intention)	Name: Matematické struktury algebry a geometrie Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures of algebra and geometry