Uniserial ring
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
A ring all indecomposable one-sided ideals of which have a unique composition series, and which splits into the direct sum of primary rings. Omission of the latter requirement leads to the definition of a generalized uniserial ring, also called a serial ring. Every generalized uniserial ring is a semi-chain ring both on the left and the right (see Semi-chain module; Semi-chain ring). Every module over a generalized uniserial ring splits into the direct sum of cyclic submodules. A ring is a generalized uniserial ring if and only if all left modules over it are semi-chain modules. An example of a uniserial ring is the ring of upper-triangular matrices over a skew-field.
How to Cite This Entry:
Uniserial ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Uniserial_ring&oldid=32110
Uniserial ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Uniserial_ring&oldid=32110
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article