Subject: Abelian Groups (2)	Code: MA263	

Semester	 Hours: C+S+L	Type	 Section	
2	2+2+0	compulsory	Algebra and Geometry - in English	

Teaching Staff in Charge	Assoc.Prof. BREAZ Simion Sorin, Ph.D., bodo@math.ubbcluj.ro
Prof. CALUGAREANU Grigore, Ph.D., calu@math.ubbcluj.ro	
Aims	Basic notions and results concerning divisibility, purity, basic subgroups and Ulm-Kaplansky invariants for abelian groups	
Content	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	
Selective References	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	Exam