JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE STRUCTURE OF SEMIPERFECT RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE STRUCTURE OF SEMIPERFECT RINGS
Han, Jun-Cheol;
  PDF(new window)
 Abstract
Let R be a ring with identity and let U(R) denote the group of all units of R. A ring R is called locally finite if every finite subset in it generates a finite semi group multiplicatively. In this paper, some results are obtained as follows: (1) for any semilocal (hence semiperfect) ring R, U(R) is a finite (resp. locally finite) group if and only if R is a finite (resp. locally finite) ring; U(R) is a locally finite group if and only if U is a locally finite group where is the full matrix ring of matrices over R for any positive integer n; in addition, if $2
 Keywords
locally finite group;locally finite ring;semilocal ring;semiperfect ring;Burnside problem for matrix group;commuting idempotents;
 Language
English
 Cited by
 References
1.
J. Cohen and K. Koh, The group of units in a compact ring, J. Pure Appl. Algebra 54 (1988), no. 2-3, 167-179 crossref(new window)

2.
J. Cohen and K. Koh, The structure of compact rings, J. Pure Appl. Algebra 77 (1992), no. 2, 117-129 crossref(new window)

3.
K. E. Eldridge and I. Fischer, D.C.C. rings with a cyclic group of units, Duke Math. J. 34 (1967), 243-248 crossref(new window)

4.
I. N. Herstein, Noncommutative Rings, The Mathematical Association of America, John Wisley and Sons, Inc., 1976

5.
C. Huh, N. K. Kim, and Y. Lee, Examples of strongly ${\pi}$-regular rings, J. Pure Appl. Algebra 189 (2004), no. 1-3, 195-210 crossref(new window)

6.
T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 1991

7.
W. K. Nicholson, Semiperfect rings with abelian group of units, Pacific J. Math. 49 (1973), 191-198 crossref(new window)