Commutative $L^{*}$-Rings
Received:June 16, 2016  Revised:November 02, 2016
Key Word: division closed   lattice order   partial order   total order   $F^{*}$-ring   $O^{*}$-ring  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.\,11271275) and the Natural Science Foundation of Shanghai Municipal (Grant No.\,13ZR1422500).
Author NameAffiliation
Jingjing MA Department of Mathematics and Statistics, University of Houston-Clear Lake, Houston TX 77058, USA 
Yuehui ZHANG Department of Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China 
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      We show that for an integral domain or a commutative local ring, it is an $L^{*}$-ring if and only if it is an $O^{*}$-ring. Some general conditions are also proved for a commutative ring that cannot be $L^{*}$.
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