## Taiwanese Journal of Mathematics

### WEAK $({C_{11}}^+)$ MODULES WITH ACC OR DCC ON ESSENTIAL SUBMODULES

Adnan Tercan

#### Abstract

In this note we study modules with $(W{C_{11}}^{+})$ property. We prove thatif $M$ satisfies $(W{C_{11}}^{+})$ and $M/(Soc M)$ has finite uniform dimensionthen $M=M_{1}\oplus M_{2}$ where $M_1$ is semisimple and $M_2$ with finiteuniform dimension. In particular, if $M$ satisfies $(W{C_{11}}^{+})$ andascending chain (respectively, descending chain) condition on essentialsubmodules then $M=M_{1}\oplus M_2$ for some semisimple submodule $M_1$and Noetherian (respectively, Artinian) submodule $M_2$.

#### Article information

Source
Taiwanese J. Math., Volume 5, Number 4 (2001), 731-738.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574991

Digital Object Identifier
doi:10.11650/twjm/1500574991

Mathematical Reviews number (MathSciNet)
MR1870043

Zentralblatt MATH identifier
1015.16001

Subjects
Primary: 16D50: Injective modules, self-injective rings [See also 16L60]

#### Citation

Tercan, Adnan. WEAK $({C_{11}}^+)$ MODULES WITH ACC OR DCC ON ESSENTIAL SUBMODULES. Taiwanese J. Math. 5 (2001), no. 4, 731--738. doi:10.11650/twjm/1500574991. https://projecteuclid.org/euclid.twjm/1500574991