MD134 Ordered algebraic structures

Faculty of Science
Spring 2009
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Mgr. Jiří Janda, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 01031
Prerequisites
Basic notions from general algebra and the theory of ordered sets.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The basic goal of the course is the introduction of the student to establish the mathematical basics of the theory of effect algebras. Some applications of the theory of effect algebras are mentioned. At the end of this course, students should be able to: understand rudiments of the theory of effect algebras; explain basic notions and relations among them. In addition, students will be able to use the methods of the theory of effect algebras to address specific issues of non-standard logics.
Syllabus
  • 1. Effect algebras 2. Examples of effect algebras - MV-algebras, ortomodular lattices 3. Lattice effect algebras 4. Archimedean lattice effect algebras 5. Compactly generated effect algebras 6. Sharply dominating effect algebras 7. Smearing of states on effect algebras
Literature
  • DVUREČENSKIJ, Anatolij. New Trends in Quantum Structures. Bratislava: Kluwer Acad. Publ., 2000, 541 pp. ISBN 0-7923-6471-6. info
Teaching methods
Lectures: theoretical explanation with practical examples oriented on solving problems for understanding of basic concepts and theorems. The lecture contains also more complex problems, homeworks. Students will be asked to have an active participation at seminars or a written homework that will be lectured at some seminar. The theme will be chosen after the negotiation with the lecturer.
Assessment methods
Lecture only. Examination is oral from the lectured material with a written preparation. The success at the examination is based on providing an exposition with respect to a chosen chapter.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught only once.
The course is also listed under the following terms Autumn 2018.
  • Enrolment Statistics (Spring 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2009/MD134