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Rings With Comparability

  • Miguel Ferrero (a1) and Alveri Sant’Ana (a2)

Abstract

The class of rings studied in this paper properly contains the class of right distributive rings which have at least one completely prime ideal in the Jacobson radical. Amongst other results we study prime and semiprime ideals, right noetherian rings with comparability and prove a structure theorem for rings with comparability. Several examples are also given.

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References

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[1] Ara, P., O’Meara, K. C. and Tyukavkin, D. V., Cancellation of projective modules over regular rings with comparability. J. Pure Appl. Algebra 107 (1996), 1938.
[2] Bessenrodt, C., Brungs, H. H. and Törner, G., Right chain rings, Part 1. Schriftenreihe des Fachbereichs Math. 181, Duisburg Univ., 1990.
[3] Brungs, H. H., Rings with a distributive lattice of right ideals. J. Algebra 40 (1976), 392400.
[4] Ferrero, M. and Törner, G., Rings with annihilator chain condition and right distributive rings. Proc. Amer. Math. Soc. 119 (1993), 401405.
[5] Ferrero, M. and Törner, G., On the ideal structure of right distributive rings. Comm. Algebra (8) 21 (1993), 26972713.
[6] Ferrero, M. and Törner, G., On waists of right distributive rings. ForumMath. 7 (1995), 419433.
[7] Mazurek, R., Distributive rings with Goldie dimension one. Comm. Algebra (3) 19 (1991), 931944.
[8] Mazurek, R. and Puczyłowski, E., On nilpotent elements of distributive rings. Comm. Algebra (2) 18 (1990), 463471.
[9] Sant’Ana, A., Anéis e Mòdulos com comparabilidade. Ph. D. thesis, Unicamp, Brazil, 1995.
[10] Stephenson, W.,Modules whose lattice of submodules is distributive. Proc. London Math. Soc. 28 (1974), 291310.
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Rings With Comparability

  • Miguel Ferrero (a1) and Alveri Sant’Ana (a2)

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