View source for Balanced ring

{{TEX|done}}{{MSC|16D}}

''on the left (right)''

A ring over which all left (right) modules are [[Balanced module|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 ring|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 ring|semi-perfect]].  A [[Noetherian ring|Noetherian]] balanced ring is an [[Artinian ring]].

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  ''Itogi Nauk. i Tekhn. Algebra Topol. Geom.'' , '''19'''  (1981)  pp. 31–134</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  C. Faith,   "Algebra" , '''1–2''' , Springer  (1973–1976)</TD></TR>
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