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Generating modules efficiently: Theorems from algebraic K-theory. (English) Zbl 0286.13012

MSC:
13D15 Grothendieck groups, \(K\)-theory and commutative rings
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
16Gxx Representation theory of associative rings and algebras
13C05 Structure, classification theorems for modules and ideals in commutative rings
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[1] Bass, H, K-theory and stable algebra, publ. math. I. H. E. S. no. 22, 5-60, (1964) · Zbl 0248.18025
[2] Bass, H, Algebraic K-theory, (1968), Benjamin Menlo Park, California · Zbl 0174.30302
[3] Bass, H, Modules which support nonsingular forms, J. algebra, 13, 246-252, (1969) · Zbl 0179.05401
[4] Bourbaki, N, Diviseurs, (1965), Hermann Paris, (“Algèbre Commutative,” Chapter 7) · Zbl 0141.03501
[5] Chase, S.U, Torsion-free modules over K[X, Y], Pacific J. math., 12, 437-447, (1962) · Zbl 0118.04404
[6] Dress, A, On the decomposition of modules, Bull. amer. math. soc., 75, 984-986, (1969) · Zbl 0201.04204
[7] Eisenbud, D; Evans, E.G, Every algebraic set in n-space is the intersection of n hypersurfaces, Invent. math., 19, 107-112, (1973) · Zbl 0287.14002
[8] Eisenbud, D; Evans, E.G, Three conjectures about modules over polynomial rings, () · Zbl 0265.13004
[9] Estes, D; Ohm, J, Stable range in commutative rings, J. algebra, 7, 343-362, (1967) · Zbl 0156.27303
[10] {\scE. G. Evans}, Krull-Schmidt and cancellation over local rings, to appear. · Zbl 0272.13006
[11] Forster, O, Über die anzahl der erzeugenden eines ideals in einem noetherschen ring, Math. Z., 84, 80-87, (1964) · Zbl 0126.27303
[12] Kaplansky, I, Infinite abelian groups, (1969), University of Michigan Press Ann Arbor · Zbl 0194.04402
[13] Kaplansky, I, Commutative rings, (1970), Allyn & Bacon Boston · Zbl 0203.34601
[14] Kronecker, L, Grundzüge eine arithmetischen theorie der algebraischen grossen, J. reine angew. math., 92, 1-123, (1882) · JFM 14.0038.02
[15] Krull, W, Über die zerlegung der hauptideale in algemeinen ringen, Math. ann., 105, 1-14, (1931) · JFM 57.0168.01
[16] Matsumura, H, Commutative algebra, (1970), Benjamin Menlo Park, California · Zbl 0211.06501
[17] Murthy, M.P, Projective modules over a class of polynomial rings, Math. Z., 88, 184-189, (1965) · Zbl 0203.04601
[18] Murthy, M.P, Generators for certain ideals in regular rings of dimension three, Comment. math. helv., 47, 179-184, (1972) · Zbl 0251.13006
[19] Orzech, Morris, Onto endomorphisms are isomorphisms, Amer. math. monthly, 78, 357-362, (1971) · Zbl 0211.06601
[20] Serre, J.-P, ()
[21] Swan, R.G, Vector bundles and projective modules, Trans. amer. math. soc., 105, 264-277, (1962) · Zbl 0109.41601
[22] Swan, R.G, The number of generators of a module, Math. Z., 102, 318-322, (1967) · Zbl 0156.27403
[23] Swan, R.G, Algebraic K-theory, () · Zbl 0193.34601
[24] van der Waerden, B.L, Review of Perron’s article “über das vahlensche beispiel zu einen satz von kronecker”, (), 276
[25] Vasconcelos, W.V, On local and stable cancellation, An. acad. brasil. ci., 37, 389-393, (1965) · Zbl 0145.27401
[26] Vasershtein, L.N, Stable rank of rings and dimensionality of topological spaces, Functional anal. appl., 5, 102-110, (1971) · Zbl 0239.16028
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