Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 111-119 (2002)

Ikeda-Nakayama Modules

Robert Wisbauer, Mohamed F. Yousif, Yiqiang Zhou

Heinrich-Heine-University, 40225 D\"{u}sseldorf, Germany, e-mail: wisbauer@math.uni-duesseldorf.de; The Ohio State University, Lima Campus, Ohio 45804, USA, e-mail: yousif.1@osu.edu; Memorial University of Newfoundland, St.John's, NF A1C 5S7, Canada, e-mail: zhou@math.mun.ca

Abstract: Let $_SM_R$ be an $(S,R)$-bimodule and denote $ l_S(A)= \{s\in S: sA=0\}$ for any submodule $A$ of $M_R$. Extending the notion of an Ikeda-Nakayama ring, we investigate the condition $ l_S(A\cap B)= l_S(A)+ l_S(B)$ for any submodules $A,B$ of $M_R$. Various characterizations and properties are derived for modules with this property. In particular, for $S=End(M_R)$, the $\pi$-injective modules are those modules $M_R$ for which $S= l_S(A)+ l_S(B)$ whenever $A\cap B=0$, and our techniques also lead to some new results on these modules.

Classification (MSC2000): 16D50; 16L60

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