Namespaces
Variants
Actions

Semi-chain module

From Encyclopedia of Mathematics
Revision as of 17:23, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A module which can be decomposed as a direct sum of chain submodules (see Chain module). All left -modules are semi-chain modules if and only if is a generalized uniserial ring.


Comments

A chain module is also called a uniserial module; correspondingly, a semi-chain module can also be called a semi-uniserial module. In [a1] the terms -uniserial and -uniserial are used for a direct sum of uniserial modules (respectively, a finite direct sum of uniserial modules).

References

[a1] C. Faith, "Algebra" , II. Ring theory , Springer (1976) pp. Chapt. 25
How to Cite This Entry:
Semi-chain module. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-chain_module&oldid=32109
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article