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Krull dimension of modules over involution rings. II
Author(s):
K.
I.
Beidar;
E.
R.
Puczylowski;
P.
F.
Smith
Journal:
Proc. Amer. Math. Soc.
125
(1997),
355-361.
MSC (1991):
Primary 16W10, 16P60
MathSciNet review:
1371115
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Abstract:
Let  be a ring with involution and invertible 2, and let  be the subring of  generated by the symmetric elements in  . The following questions of Lanski are answered positively: - (i)
- Must
 have Krull dimension when  does? - (ii)
- Is every Artinian
 -module Artinian as an  -module?
References:
- [1]
- S.A. Amitsur, Rings with involution, Israel J. Math. 6 (1968), 99-106. MR 39:256
- [2]
- K.I. Beidar, E.R. Puczy{\l}owski and P.F. Smith, Krull dimension of modules over involution rings, Proc. Amer. Math. Soc. 121 (1994), 391-397. MR 94h:16064
- [3]
- K.I. Beidar and V.T. Markov, A semiprime PI-ring having a faithful module with Krull dimension is a Goldie ring, Russian Math. Survey 48 (1993), 141-142. MR 94m:16023
- [4]
- C.L. Chuang and P.H. Lee, Noetherian rings with involution, Chinese J. Math. 5 (1977), 15-19. MR 56:12053
- [5]
- R. Gordon and J.C. Robson, Krull dimension, Memoirs Amer. Math. Soc., No. 133, American Mathematical Society, Providence, 1973. MR 50:4664
- [6]
- I.N. Herstein, Topics in ring theory, Univ. Chicago Press, Chicago, 1969. MR 42:6018
- [7]
- C. Lanski, On the relationship of a ring and the subring generated by its symmetric elements, Pacific J. Math. 44 (1973), 581-592. MR 48:331
- [8]
- C. Lanski, Chain conditions in rings with involution, J. London Math. Soc. 9 (1974), 93-102. MR 50:13123
- [9]
- C. Lanski, Chain conditions in rings with involution II, J. London Math. Soc. 18 (1978), 421-428. MR 80a:16024
- [10]
- C. Lanski, Gabriel dimension and rings with involution, Houston Math. J. 4 (1978), 397-415. MR 80a:16025
- [11]
- P.H. Lee On subrings of rings with involution, Pacific J. Math. 60 (1975), 131-147. MR 53:519
- [12]
- V.T. Markov, On PI rings having a faithful module with Krull dimension (to appear).
- [13]
- S. Montgomery, A structure theorem and a positive-definiteness condition in rings with involution, J. Algebra 43 (1976), 181-192. MR 54:12821
- [14]
- S. Montgomery, Fixed rings of finite automorphism groups of associative rings, Lectures Notes in Math. Vol. 818, Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 81j:16041
- [15]
- L.H. Rowen, On rings with central polynomials, J. Algebra 31 (1974), 393-426. MR 50:2237
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Additional Information:
K.
I.
Beidar
Affiliation:
Department of Mathematics, Moscow State University, Moscow, Russia
Address at time of publication:
National Cheng--Kung University, Department of Mathematics, Tainan, Taiwan
Email:
t14270@sparc1.cc.ncku.edu.tw
E.
R.
Puczylowski
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Poland
Email:
edmundp@mimuw.edu.pl
P.
F.
Smith
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow, Scotland
Email:
pfs@maths.gla.ac.uk
DOI:
10.1090/S0002-9939-97-03724-6
PII:
S 0002-9939(97)03724-6
Received by editor(s):
August 23, 1995
Additional Notes:
The research of the second author was partially supported by KBN grant 2 P301 035 06.
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1997,
American Mathematical Society
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