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

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10101 Pure mathematics
• Country of publisher: Canada
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• RIV identification code: RIV/00216224:14310/02:00006486
• Organization unit: Faculty of Science
• ISSN: 1703-0048
• Keywords in English: simple quantale; semisimple quantale
• Tags: semisimple quantale, Simple quantale
• Tags: International impact, Reviewed

Abstract

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.

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