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Lifting idempotents and exchange rings. (English) Zbl 0352.16006


MSC:

16U60 Units, groups of units (associative rings and algebras)
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16D40 Free, projective, and flat modules and ideals in associative algebras
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References:

[1] Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466 – 488. · Zbl 0094.02201
[2] Peter Crawley and Bjarni Jónsson, Refinements for infinite direct decompositions of algebraic systems, Pacific J. Math. 14 (1964), 797 – 855. · Zbl 0134.25504
[3] Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964. · Zbl 0144.27103
[4] Irving Kaplansky, Projective modules, Ann. of Math (2) 68 (1958), 372 – 377. · Zbl 0083.25802 · doi:10.2307/1970252
[5] G. S. Monk, A characterization of exchange rings, Proc. Amer. Math. Soc. 35 (1972), 349 – 353. · Zbl 0258.16030
[6] Bruno J. Mueller, On semi-perfect rings, Illinois J. Math. 14 (1970), 464 – 467. · Zbl 0197.30903
[7] W. K. Nicholson, Semiregular modules and rings, Canad. J. Math. 28 (1976), no. 5, 1105 – 1120. · Zbl 0317.16005 · doi:10.4153/CJM-1976-109-2
[8] W. A. Shutters, Exchange rings and P-exchange rings, Notices Amer. Math. Soc. 21 (1974), A-590. Abstract #74T-A242.
[9] R. B. Warfield Jr., A Krull-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969), 460 – 465. · Zbl 0176.31401
[10] R. B. Warfield Jr., Exchange rings and decompositions of modules, Math. Ann. 199 (1972), 31 – 36. · Zbl 0228.16012 · doi:10.1007/BF01419573
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