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On Conrad’s partial order relation on semiprime rings and on semigroups. (English) Zbl 0382.06019

MSC:
06F25 Ordered rings, algebras, modules
06F05 Ordered semigroups and monoids
06B23 Complete lattices, completions
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References:
[1] Abian, A.,Direct product decomposition of commutative semisimple rings, Proc. Amer. Math. Soc. 24 (1970) 502–507. · Zbl 0207.05002
[2] Bertiaume, P.,The injective envelope of S-sets, Canad. Math. Bull. 10 (1967) 261–273. · Zbl 0149.26103
[3] Burgess, W.D. and Raphael, R,Abian’s order relation and orthogonal completeness for reduced rings, Pacific J. Math. 54 (1974) 55–64. · Zbl 0255.16008
[4] —-,Complete and orthogonally complete rings, Canad. J. Math. 27 (1975) 884–892. · Zbl 0316.13004
[5] —-,Sur deux notions de complĂ©tude dans les anneaux semipremiers, C.R. Acad. Sci. Paris 283 (1976) 927–929. · Zbl 0342.16008
[6] Clifford, A.H. and Preston, G.B.,The Algebraic Theory of Semigroups, Vol I. American Mathematical Society, Providence, R.I., 1961. · Zbl 0111.03403
[7] Conrad, P.F.,The hulls of semiprime rings, Bull. Austral. Math. Soc. 12 (1975) 311–314. · Zbl 0297.16003
[8] Conrad, P.F.,The hulls of semiprime rings, typescript, 1976.
[9] Lambek, J.,Lectures on Rings and Modules. Blaisdell, Waltham, Mass, Toronto and London, 1966. · Zbl 0143.26403
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