Strict radical classes of commutative rings
HTML articles powered by AMS MathViewer
- by N. R. McConnell
- Proc. Amer. Math. Soc. 118 (1993), 27-35
- DOI: https://doi.org/10.1090/S0002-9939-1993-1126200-X
- PDF | Request permission
Abstract:
We classify strongly hereditary strict radical classes for commutative rings and give some results for supernilpotent strict radical classes and strict radical classes contained in the nil radical.References
- E. P. Armendariz, Hereditary subradical of the lower Baer radical, Publ. Math. Debrecen 15 (1968), 91–93. MR 237551, DOI 10.5486/pmd.1968.15.1-4.13
- N. Divinsky, Unequivocal rings, Canadian J. Math. 27 (1975), no. 3, 679–690. MR 374180, DOI 10.4153/CJM-1975-076-5
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- B. J. Gardner, A note on radicals and polynomial rings, Math. Scand. 31 (1972), 83–88. MR 318206, DOI 10.7146/math.scand.a-11414
- B. J. Gardner, Radical classes of regular rings with Artinian primitive images, Pacific J. Math. 99 (1982), no. 2, 337–349. MR 658064
- L. C. A. van Leeuwen, Complements of radicals in the class of hereditarily Artinian rings, Acta Sci. Math. (Szeged) 39 (1977), no. 3-4, 313–318. MR 491791
- N. R. McConnell, Hereditary and strict domains for radical classes of associative rings, Bull. Austral. Math. Soc. 41 (1990), no. 2, 255–269. MR 1041672, DOI 10.1017/S0004972700018086
- A. D. Sands, On dependence and independence among radical properties, Rings, modules and radicals (Hobart, 1987) Pitman Res. Notes Math. Ser., vol. 204, Longman Sci. Tech., Harlow, 1989, pp. 125–141. MR 1035734
- Robert L. Snider, Lattices of radicals, Pacific J. Math. 40 (1972), 207–220. MR 308175
- Patrick N. Stewart, Strongly hereditary radical classes, J. London Math. Soc. (2) 4 (1971/72), 499–509. MR 306250, DOI 10.1112/jlms/s2-4.3.499
- Patrick N. Stewart, Strict radical classes of associative rings, Proc. Amer. Math. Soc. 39 (1973), 273–278. MR 313296, DOI 10.1090/S0002-9939-1973-0313296-5
- A. Widiger and R. Wiegandt, Theory of radicals for hereditarily Artinian rings, Acta Sci. Math. (Szeged) 39 (1977), no. 3-4, 303–312. MR 498662
- Richard Wiegandt, Radical and semisimple classes of rings, Queen’s Papers in Pure and Applied Mathematics, No. 37, Queen’s University, Kingston, Ont., 1974. MR 0349734
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 27-35
- MSC: Primary 13A10; Secondary 16N80
- DOI: https://doi.org/10.1090/S0002-9939-1993-1126200-X
- MathSciNet review: 1126200