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| MATI7251 | Lattice Ordered Monoids | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Ümit ERTUĞRUL | | Co-Lecturer | Doç. Dr. Ümit Ertuğrul, Doç. Dr. Gül Deniz Çaylı | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to investigate the fundamental concepts of po-gropoid, l-grupoid and l-monoid. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | The students will learn the concepts of partially ordered groupoids, lattice ordered groupoids and lattice ordered monoids. | 1 - 2 - 3 | 1, | | PO - 2 : | The students will investigate the basic properties of lattice ordered groupoids, residuation, integral l- groupoids, maximal and prime elements, abstract ideal theory. | 1 - 2 - 3 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Po-groupoids, Examples of l- groupoids and l- monoids, Residuations, Integral l- groupoids, Maximal and prime elements, Abstract Ideal Theory, Fundamental Theorem of Ideal Theory, Frobenius l-monoids, Postulates for relation algebras. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Po-groupoids | | | Week 2 | Divisibility monoids | | | Week 3 | Archimedean monoids | | | Week 4 | Examples of l-groupoids and l-monoids | | | Week 5 | Residuation | | | Week 6 | Elementary applications | | | Week 7 | Integral l-groupoids | | | Week 8 | Commutation lattices | | | Week 9 | Mid-term exam | | | Week 10 | Maximal and prime elements | | | Week 11 | Abstract ideal theory | | | Week 12 | Fundamental theorem of ideal theory | | | Week 13 | Frobenius l-monoids | | | Week 14 | Algebra of relations | | | Week 15 | Postulates for relation algebras | | | Week 16 | End-of-term exam | | | |
| 1 | Birkhoff, G. 1948; Lattice Theory, American Mathematical Society Colloquium Publishers, Providence, RI | | | |
| 1 | Fuchs, L. 1963; Partially Ordered Algebraic Systems, Pergamon Press, Oxford, New York | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 26/04/2021 | 2 | 30 | | In-term studies (second mid-term exam) | 13 | 24/05/2021 | 2 | 20 | | End-of-term exam | 16 | 21/06/2021 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 3 | 14 | 42 | | Arasınav için hazırlık | 10 | 8 | 80 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 9.5 | 6 | 57 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 225 |
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