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References
M. Auslander, “On regular group rings,”Proc. Amer. Math. Soc.,8, 658–664 (1957).
A. H. Clifford and G. B. Preston,The Algebraic Theory of Semigroups, Vols. 1, 2, Amer. Math. Soc., Providence (1964, 1967).
General Algebra [in Russian], Vol. 1, Nauka, Moscow (1990).
C. W. Curtis and I. Reiner,Representation Theory of Finite Groups and Associative Algebras, John Wiley and Sons, New York-London (1962).
C. Faith,Algebra: Rings, Modules, and Categories, Vols. 1, 2, Springer-Verlag (1973, 1976).
J. W. Fisher, “Von Neumann regular rings versus V-rings,” In:Ring Theory. Proc. Oklahoma Conf., Lect. Notes, Vol. 7, Marcel Dekker, New York (1974), pp. 101–119.
R. Gilmer,Commutative Semigroup Rings, Chicago Univ. Press (1984).
R. Gilmer and M. L. Teply, “Idempotents of commutative semigroup rings,”Houston J. Math.,3, 369–385 (1977).
K. R. Goodearl,Von Neumann Regular Rings, Pitman, London (1979).
V. Gupta, “Weaklyπ-regular rings and group rings,”Math. J. Okayama Univ.,19, No. 2, 123–127 (1977).
J. Janesski and J. Weissglass, “Regularity of semilattice sums of rings,”Proc. Amer. Math. Soc.,39, 479–482 (1973).
A. V. Kelarev, “On regular semigroup rings,”Semigroup Forum,40, No. 1, 113–114 (1990).
I. B. Kozhukhov, “A note on the weak regularity of semigroup rings,”Semigroup Forum (in press).
J. McLaughlin, “A note on regular group rings,”Mich. Math. J.,5, 127–128 (1958).
F. Li, “On the weak regularity of semigroup rings,”Semigroup Forum,48, No. 2, 152–162 (1994).
F. Li, “The regularity of Munn rings and semigroup rings,”Acta Math. Sinica, New Series,11, No. 1, 53–61 (1995).
A. V. Mikhalev and A. E. Zalesski, “Group rings,” In:Progress in Science and Technology. Series on Contemporary Problems in Mathematics. Itogi Nauki i Tekhn., Vol. 2, All-Union Institute for Scientific and Technical Information, Akad. Nauk SSSR, Moscow (1973), pp. 5–118.
S. V. Mihovski, “On strongly regular group rings,”Izv. Mat. Inst. Bolg. Akad. Nauk,14, 67–72 (1973).
W. D. Munn, “On the regularity of certain semigroup algebras,” In:Semigroups, Academic Press, London (1980), pp. 207–224.
J. Okninski, “On regular semigroup rings,”Proc. R. Soc. Edinburgh, A,99, 145–151 (1984).
J. Okninski,Semigroup Algebras, Marcel Dekker (1991).
J. S. Ponizovskii, “Semigroup rings,”Semigroup Forum,36, 1–46 (1987).
L. A. Skornyakov,Elements of Common Algebra [in Russian], Nauka, Moscow (1983).
A. A. Tuganbaev, “Distributive monoid algebras,”Mat. Zametki,51, No. 2, 101–108 (1992).
N. Vanaja, “A note on weakly regular rings,”Notices Amer. Math. Soc.,17, No. 806 (1970).
O. E. Villamayor, “On weak dimension of algebras,”Pacif. J. Math.,9, 941–951 (1959).
J. Weissglass, “Regularity of semigroup rings,”Proc. Amer. Math. Soc.,25, 499–503 (1970).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 46, Algebra-8, 1997.
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Kozhukhov, I.B. Technique of semigroup ring theory: Regular semigroup rings. J Math Sci 95, 2317–2327 (1999). https://doi.org/10.1007/BF02169100
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DOI: https://doi.org/10.1007/BF02169100