Abstract
We show that the direct product of an infinite set of 2-primal rings (or even rings satisfying (PS I)) need not be a 2-primal ring, and we develop some sufficient conditions on the rings for their direct product to be 2-primal. We also show that the ring of formal power series over a 2-primal ring (or even a ring satisfying (PS I)) need not be 2-primal.
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References
Birkenmeier, G. F.; Heatherly, H. E.; Lee, E. K.; Completely prime ideals and associated radicals; in Jain, S. K.; Rizvi, S. T. (eds.); Ring Theory: Proc. Biennial Ohio State-Denison Conference,May 1992, World Scientific; Singapore and River Edge, N.J. (1993), 102–129, 373.
Birkenmeier, G. F.; Heatherly, H. E.; Lee, E. K.; Completely prime ideals and radicals in near-rings; in Fong, Y.; Bell, H. E., Ke. W.-F.; Mason, G.; Pilz, G. (eds.); Near-Rings and Near-Fields: Proc. Conference on Near-Rings and Near-Fields,Fredericton, New Brunswick. Canada, July 1993, Kluwer; Dordrecht, Boston, London (1995), 6373.
Fisher, J. W., On the nilpotency of nil subrings, Canad. J. Math 22 (1970), 1211–1216.
Hirano, Y., Some studies on strongly π-regular rings, Math. J. Oka-yama Univ. 20 (1978), 141–149.
Hirano, Y.; van Huynh, D.; Park, J. K.; On rings whose prime radical contains all nilpotent elements of index two, Arch. Math 66 (1996). 360–365.
Huh, C.; Kim, H. K.; Lee, Y.; Questions on 2-primal rings, Department of Mathematics, Busan National University, Busan 609–735. South Korea (preprint).
Jacobson, N., Structure of Rings, second edition, AMS Collog. Pub. 37; American Mathematical Society; Providence, R.I. (1964).
Lam, T. Y., A First Course in Noncommutative Rings, Graduate Texts in Mathematics 131, Springer-Verlag; New York, N.Y. (1991).
Lam, T. Y., Exercises in Classical Ring Theory, Problem Books in Mathematics, Springer-Verlag; New York, N.Y. (1995).
Shin, G., Prime ideals and sheaf representations of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43–60.
Sun, S.-H., Noncommutative, rings in which every prime ideal is contained in a unique maximal ideal,J. Pure Appl. Algebra 76 (1991). 179–192.
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Marks, G. (1997). Direct Product and Power Series Formations Over 2-Primal Rings. In: Jain, S.K., Rizvi, S.T. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1978-1_19
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DOI: https://doi.org/10.1007/978-1-4612-1978-1_19
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7364-6
Online ISBN: 978-1-4612-1978-1
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