The closure of radical classes under finite subdirect products

B. J. Gardner; Patrick N. Stewart

Compositio Mathematica (1982)

  • Volume: 46, Issue: 2, page 145-158
  • ISSN: 0010-437X

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Gardner, B. J., and Stewart, Patrick N.. "The closure of radical classes under finite subdirect products." Compositio Mathematica 46.2 (1982): 145-158. <http://eudml.org/doc/89550>.

@article{Gardner1982,
author = {Gardner, B. J., Stewart, Patrick N.},
journal = {Compositio Mathematica},
keywords = {finite subdirect products; hereditary radical classes; idempotent rings; annihilator ideals; homomorphically closed class of rings; upper radical; lower radical class},
language = {eng},
number = {2},
pages = {145-158},
publisher = {Martinus Nijhoff Publishers},
title = {The closure of radical classes under finite subdirect products},
url = {http://eudml.org/doc/89550},
volume = {46},
year = {1982},
}

TY - JOUR
AU - Gardner, B. J.
AU - Stewart, Patrick N.
TI - The closure of radical classes under finite subdirect products
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 46
IS - 2
SP - 145
EP - 158
LA - eng
KW - finite subdirect products; hereditary radical classes; idempotent rings; annihilator ideals; homomorphically closed class of rings; upper radical; lower radical class
UR - http://eudml.org/doc/89550
ER -

References

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  1. [1] V.A. Andrunakievič: Radicals of associative rings. I. Amer. Math. Soc. Transl. (2) 52, 95-128. (Russian original: Mat. Sb. 44 (1958) 179-212.) Zbl0080.02602MR98765
  2. [2] E.P. Armendariz and J.W. Fisher: Regular P.I. rings. Proc. Amer. Math. Soc.39 (1973) 247-251. Zbl0264.16010MR313305
  3. [3] R. Baer: Linear Algebra and Projective Geometry. Academic Press, New York1952. Zbl0049.38103MR52795
  4. [4] R.C. Courter: Rings all of whose factors are semiprime. Canad. Math. Bull.12 (1969) 417-426. Zbl0185.08801MR254099
  5. [5] R. Dark and A.H. Rhemtulla: On Ro-closed classes, and finitely generated groups. Canad. J. Math22 (1970) 176-184. Zbl0215.10401MR257211
  6. [6] N. Divinsky: Unequivocal rings. Canad. J. Math.27 (1975) 679-690. Zbl0309.16007MR374180
  7. [7] L. Fuchs: On subdirect unions. I. Acta Math. Adad. Sci. Hungar.3 (1952) 103-119. Zbl0047.03003MR52395
  8. [8] B.J. Gardner: Polynomial identities and radicals. Compositio Math.35 (1977) 269-279. Zbl0328.16008MR453798
  9. [9] A.G. Heinicke: Subdirect sums, hereditary radicals, and structure spaces. Proc. Amer. Math. Soc.25 (1970) 29-33. Zbl0212.37603MR255609
  10. [10] I. Kaplansky: Rings with a polynomial identity. Bull. Amer. Math. Soc.54 (1948) 575-580. Zbl0032.00701MR25451
  11. [11] S.R. Kogalovskii: Structural characteristics of universal classes. Sibirsk. Mat. Ž.4 (1963) 97-119 (in Russian). MR147393
  12. [12] W.G. Leavitt: A minimally embeddable ring. Period. Math. Hungar.12 (1981) 129-140. Zbl0439.16006MR603406
  13. [13] L.C.A. Van Leeuwen: Upper radical constructions for associative rings, Ring Theory (Proc. Conf. Univ. Antwerp, 1977), Dekker, New York, 1978, pp. 147-154. Zbl0389.16002MR522820
  14. [14] R. Raphael: Fully idempotent factorization rings. Commun. Algebra7 (1979) 547-563. Zbl0404.16005MR524268
  15. [15] A. Suliński: Some questions in the general theory of radicals. Mat. Sb.44 (1958) 273-286 (in Russian). Zbl0080.25802MR98119
  16. [16] F.A. Szász: A second almost subidempotent radical for rings. Math. Nachr.66 (1975) 283-289. Zbl0305.16004MR379564

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