Martinez Lopez, Consuelo A new order relation for JB-algebras. (English) Zbl 0808.46072 Ann. Sci. Univ. Blaise Pascal Clermont-Ferrand II 97, Math. 27, 135-138 (1991). For a Jordan ring for which \(2x= 0\) only if \(x=0\), define \(x\leq y\) iff \(xy= x^ 2\), \(x^ 2 y= xy^ 2= x^ 3\). The author gives conditions for \(\leq\) to be a partial order; in particular, this is so for a JB- algebra. Reviewer: E.J.Barbeau (Toronto) MSC: 46H70 Nonassociative topological algebras 17C65 Jordan structures on Banach spaces and algebras 06A06 Partial orders, general Keywords:Boolean ring; partially ordered ring; Jordan ring; JB-algebra PDFBibTeX XMLCite \textit{C. Martinez Lopez}, Ann. Sci. Univ. Blaise Pascal Clermont-Ferrand II, Math. 97(27), 135--138 (1991; Zbl 0808.46072) Full Text: Numdam EuDML References: [1] 1 A. Abian , ” Direct product decomposition of commutatif semisimple ring ”, Proc. Amer. Math. Soc. 24 , ( 1970 ), 502 - 507 . MR 258815 | Zbl 0207.05002 · Zbl 0207.05002 · doi:10.2307/2037396 [2] 2 A. Abain , Order in a special class of rings and a structure theorem , Proc. Amer. Math. Soc. 52 ( 1975 ) 45 - 49 . MR 374222 | Zbl 0314.17013 · Zbl 0314.17013 · doi:10.2307/2040097 [3] 3 L. Bunce , On a compact action in JB-algebras , Proc. Edimburgh Math. Soc. 26 , ( 1983 ), 353 - 360 . MR 722566 | Zbl 0531.46038 · Zbl 0531.46038 · doi:10.1017/S0013091500004429 [4] 4 M. Chacron , Direct product of division rings and a paper of Abian , Proc. Amer. Math. Soc. 29 , ( 1971 ), 259 - 262 . MR 274512 | Zbl 0251.16014 · Zbl 0251.16014 · doi:10.2307/2038122 [5] 5 S. Gonzalez , C. Martinez , Order relation in Jordan rings and a structure theorem . Proc. Amer. Math. Soc. 98 , ( 1986 ), 379 - 388 . MR 857926 | Zbl 0607.17012 · Zbl 0607.17012 · doi:10.2307/2046187 [6] 6 M.C. Myung , L.R. Gimenez , Proc. Amer. Math. Soc. 47 , ( 1975 ), 53 - 60 MR 354796 | Zbl 0301.17004 · Zbl 0301.17004 · doi:10.2307/2040207 [7] 7 K.A. Zhevlakov , A.M. Slinko , I.P. Schestakov and A.I. Shirshov , Rings that are nearly associative , Academic Press , ( 1982 ). MR 668355 | Zbl 0487.17001 · Zbl 0487.17001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.