000			01967cam a2200313 a 4500
001			549463
005			20250612184114.0
008			880927s1989 gw a b 001 0 eng
020			_a9783540642398
040			_aCSL _cCSL
041	1		_aeng _hfre
084			_aB2 M9 NBHM _qCSL
100	1		_aBourbaki, Nicolas. _eauthor.
245	1	0	_aCommutative algebra : _bchapters 1-7
260			_aBerlin : _bSpringer-Verlag, _c1989.
300			_axxiv, 625 p. : _bill. ; _c24 cm.
440			_vElements of mathematics
490	1		_aElements of mathematics
500			_aTranslation of: Algebre commutative.
504			_aIncludes bibliographical references (p. 603-606) and indexes.
520			_aThis is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.
650		0	_aCommutative algebra.
650		0	_aalgebraic geometry _9409661
650		0	_aarithmetical _9812766
650		0	_acommutative algebra
650		0	_adivisors _9812767
800	1		_aBourbaki, Nicolas. _tElements of mathematics. _9812768
942			_2CC _n0 _cTEXL _hB2 M9 NBHM
999			_c1431678 _d1431678