Abstract
For arbitrary modules A and B we introduce and study the notion of a fully idempotent Hom (A, B). As a corollary we obtain some well-known properties of fully idempotent rings and modules.
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References
V. Camillo and Y. F. Xiao, “Weakly Regular Rings,” Commun. Algebra 22(10), 4095–4112 (1994).
R. R. Andruszkiewicz and E. R. Puczyłowski, “Right Fully Idempotent Rings Need not be Left Fully Idempotent,” Glasgow Math. J. 37(2), 155–157 (1995).
V. S. Ramamurthi, “Weakly Regular Rings,” Canad. Math. Bull. 16, 317–321 (1973).
A. A. Tuganbaev, Theory of Rings. Arithmetic Modules and Rings (MTsNMO, Moscow, 2009) [in Russian].
A. A. Tuganbaev, Rings Close to Regular (Kluwer Academic Publishers, Dordrecht, 2002).
A. A. Tuganbaev, “Semiregular, Weakly Regular, and π-Regular Rings,” J. Math. Sci. (New York) 109(3), 1509–1588 (2002).
Y. Hirano, “Regular Modules and V-Modules,” Hiroshima Math. J. 11(1), 125–142 (1981).
Y. Hirano, “Regular Modules and V-Modules. II,” Math. J. Okayama Univ. 23(2), 131–135 (1981).
V. S. Ramamurthi, “ANote on Regular Modules,” Bull. Austral. Math. Soc. 11(3), 359–364 (1974).
M. Jayaraman and N. Vanaja, “Generalization of Regular Modules,” Commun. Algebra 35(11), 3331–3345 (2007).
T. Mabuchi, “Weakly Regular Modules,” Osaka J. Math. 17(1), 35–40 (1980).
J. Zelmanowitz, “Regular Modules,” Trans. Amer. Math. Soc. 163, 341–355 (1972).
G. Azumaya, “Some Characterizations of Regular Modules,” Publ. Matem. Barc. 34(2), 241–248 (1990).
W. K. Nicholson and Y. Zhou, “Semiregular Morphisms,” Commun. Algebra 34(1), 219–233 (2006).
F. Kasch and A. Mader, “Regularity and Substructures of Hom,” Commun. Algebra 34(4), 1459–1478 (2006).
F. Kasch, “Regular Substructures of Hom,” Appl. Categ. Structur. 16(1–2), 159–166 (2008).
R. Wisbauer, Foundations of Module and Ring Theory. A Handbook for Study and Research. Revised and updated by Engl. ed. (Gordon and Breach Science Publishers, Philadelphia, 1991).
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Original Russian Text © A.N. Abyzov, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 8, pp. 3–7.
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Abyzov, A.N. Fully idempotent homomorphisms. Russ Math. 55, 1–6 (2011). https://doi.org/10.3103/S1066369X11080019
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DOI: https://doi.org/10.3103/S1066369X11080019