This article is cited in 2 papers

$RD$-formulas and $W$-rings

G. E. Puninskii

D. Mendeleev University of Chemical Technology of Russia

Abstract: We study rings over which any finitely presented module is a direct summand of a direct sum of cyclic cyclically presented modules (Warfield rings). We characterize these rings in matrix terms. We clarify a number of properties of Warfield rings including their complete characterization in some special cases. We prove the presence of special (deeper than $pp$) elimination of quantifiers in module theory over these rings.

UDC: 512.553+512.55.0

Received: 23.04.1992

 English version: Mathematical Notes, 1993, 53:1, 66–71

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