Regular elements in rings with involution

Author:
Charles Lanski

Journal:
Trans. Amer. Math. Soc. **195** (1974), 317-325

MSC:
Primary 16A28

MathSciNet review:
0354760

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Abstract: The purpose of this paper is to determine when a symmetric element, regular with respect to other symmetries, is regular in the ring. This result is true for simple rings, for prime rings with either Goldie chain condition, and for semiprime Goldie rings. Examples are given to show that these results are the best that can be hoped for.

**[1]**I. N. Herstein,*Topics in ring theory*, The University of Chicago Press, Chicago, Ill.-London, 1969. MR**0271135****[2]**I. N. Herstein,*On rings with involution*, Canad. J. Math.**26**(1974), 794–799. MR**0360674****[3]**Nathan Jacobson,*Structure of rings*, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964. MR**0222106****[4]**Charles Lanski,*Rings with involution whose symmetric elements are regular*, Proc. Amer. Math. Soc.**33**(1972), 264–270. MR**0292889**, 10.1090/S0002-9939-1972-0292889-7**[5]**Charles Lanski,*On the relationship of a ring and the subring generated by its symmetric elements*, Pacific J. Math.**44**(1973), 581–592. MR**0321966****[6]**Wallace S. Martindale III,*Prime rings satisfying a generalized polynomial identity*, J. Algebra**12**(1969), 576–584. MR**0238897****[7]**Wallace S. Martindale III,*Prime rings with involution and generalized polynomial identities*, J. Algebra**22**(1972), 502–516. MR**0306245****[8]**Louis Rowen,*Some results on the center of a ring with polynomial identity*, Bull. Amer. Math. Soc.**79**(1973), 219–223. MR**0309996**, 10.1090/S0002-9904-1973-13162-3

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0354760-8

Article copyright:
© Copyright 1974
American Mathematical Society