Geodesic
Equationally Compact Artinian Rings
Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 273-283

Voir la notice de l'article provenant de la source Cambridge University Press

By a Noetherian (Artinian) ring = (R; + , —, 0, ·) we mean an associative ring satisfying the ascending (descending) chain condition on left ideals. An arbitrary ring is said to be equationally compact if every system of ring polynomial equations with constants in is simultaneously solvable in provided every finite subset is. (The reader is referred to [2; 8; 13; 14] for terminology and relevant results on equational compactness, and to [4] for unreferenced ring-theoretical results.) In this report a characterization of equationally compact Artinian rings is given - roughly speaking, these are the finite direct sums of finite rings and Prüfer groups; as consequences it is shown that an equationally compact ring satisfying both chain conditions is always finite, as is any Artinian ring which is a compact topological ring. 
Haley, David K. Equationally Compact Artinian Rings. Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 273-283. doi: 10.4153/CJM-1973-027-x
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