Isomorphisms of prime Goldie semiprincipal left ideal rings
HTML articles powered by AMS MathViewer
- by Kenneth G. Wolfson PDF
- Proc. Amer. Math. Soc. 104 (1988), 25-29 Request permission
Abstract:
A prime (left) Goldie semiprincipal left ideal ring is the endomorphism ring $E(F,A)$ of a free module $A$, of finite rank, over a (left) Ore domain $F$. We examine the uniqueness of the module $(F,A)$ in the sense of determining necessary and sufficient conditions that every isomorphism of $E(F,A)$ is induced by a semilinear module isomorphism of $(F,A)$.References
- Reinhold Baer, Linear algebra and projective geometry, Academic Press, Inc., New York, N.Y., 1952. MR 0052795
- A. W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Soc. (3) 10 (1960), 201–220. MR 111766, DOI 10.1112/plms/s3-10.1.201
- A. W. Goldie, Non-commutative principal ideal rings, Arch. Math. 13 (1962), 213–221. MR 140532, DOI 10.1007/BF01650068
- I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
- Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, 190 Hope Street, Providence, R.I., 1956. MR 0081264
- A. V. Jategaonkar, Left principal ideal rings, Lecture Notes in Mathematics, Vol. 123, Springer-Verlag, Berlin-New York, 1970. MR 0263850
- Wolfgang Liebert, Endomorphism rings of free modules over principal ideal domains, Duke Math. J. 41 (1974), 323–328. MR 346015
- J. C. Robson, Rings in which finitely generated right ideals are principal, Proc. London Math. Soc. (3) 17 (1967), 617–628. MR 217109, DOI 10.1112/plms/s3-17.4.617
- Richard G. Swan, Projective modules over group rings and maximal orders, Ann. of Math. (2) 76 (1962), 55–61. MR 139635, DOI 10.2307/1970264
- Kenneth G. Wolfson, Isomorphisms of prime Goldie semi-principal left ideal rings. II, Canad. Math. Bull. 31 (1988), no. 3, 374–379. MR 956370, DOI 10.4153/CMB-1988-053-3
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 25-29
- MSC: Primary 16A65; Secondary 16A04, 16A34
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958036-2
- MathSciNet review: 958036