Balanced ring
From Encyclopedia of Mathematics
2020 Mathematics Subject Classification: Primary: 16D [MSN][ZBL]
on the left (right)
A ring over which all left (right) modules are balanced. A ring is balanced on the left if and only if all its quotient rings are QF-$1$-rings, that is, if all the exact left modules over it are balanced. In particular, a ring is balanced if all its quotient rings are quasi-Frobenius. Every balanced ring can be split into a direct sum of a uniserial ring and rings of matrices over local rings of a special type. Every balanced ring is semi-perfect. A Noetherian balanced ring is an Artinian ring.
References
| [1] | Itogi Nauk. i Tekhn. Algebra Topol. Geom. , 19 (1981) pp. 31–134 |
| [2] | C. Faith, "Algebra" , 1–2 , Springer (1973–1976) |
How to Cite This Entry:
Balanced ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Balanced_ring&oldid=35544
Balanced ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Balanced_ring&oldid=35544
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article