000			01936nam a22002537i 4500
005			20250715123320.0
008			250715s2021 uk a|||fr|||| 00| 0 eng d
020			_a9781108958233
040			_aEG-GaU‬‬ _cEG-GaU‬‬ _dEG-GaU‬‬ _erda
082	0	4	_223 _a512 _bA.P.A
100	1		_aAluffi, Paolo, _eauthor _960247
245	1	0	_aAlgebra : _bNotes from the Underground / _cPaolo Aluffi.
264		1	_aCambridge : _bCambridge University Press, _c2021
300			_a472 pages : _billustrations ; _c24 cm.
336			_2rdacontent _atext _btxt
337			_2rdamedia _aunmediated _bn
338			_2rdacarrier _avolume _bnc
520			_aFrom rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.
650		0	_aAlgebra _v Study and teaching _xTextbooks. _960248
650		0	_aModules (Algebra) _v Study and teaching. _960249
650		0	_aCategorical algebra _vStudy and teaching. _960250
942			_2ddc _cBK
999			_c10993 _d10993