"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Abelian Groups (2) |
ter |
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| Teaching Staff in Charge |
Assoc.Prof. BREAZ Simion Sorin, Ph.D., bodo math.ubbcluj.roProf. CALUGAREANU Grigore, Ph.D., calu math.ubbcluj.ro |
| Aims |
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Basic notions and results concerning divisibility, purity, basic subgroups and Ulm-Kaplansky invariants for abelian groups. |
| Content |
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Basic knowledges concerning divisibility (equivalence to injectivity, structure theorem), purity (the notion of purity in lattices, characterizations of purity for subgroups), basic subgroups (existence and uniqueness up to an isomorphism), Ulm-Kaplansky invariants and Ulm's theorem. |
| References |
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1. L. FUCHS: Infinite Abelian Groups, vol.1, Academic Press, 1970.
2. G. CALUGAREANU: Introducere laticiala in teoria grupurilor abeliene, Editura Expert, 1994. 3. G. CALUGAREANU, S. BREAZ, C. MODOI, C. PELEA, D. VALCAN: Exercises in abelian group theory, Kluwer Academic Publishers Group, Dordrecht, 2003 4. J.J. ROTMAN: An introduction to the theory of groups. Fourth edition. Springer-Verlag, New York, 1995. 5. J.L. ALPERIN, R.B. BELL: Groups and representations. Springer-Verlag, New York, 1995. |
| Assessment |
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Exam. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |