caa a22 4500 38803923X CHVBK 20180307125016.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.2307/2586842 doi S0022481200015000 pii (NATIONALLICENCE)cambridge-10.2307/2586842 Prest Mike Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK, E-mail: mprest@ma.man.ac.uk The representation theories of elementarily equivalent rings [Elektronische Daten] [Mike Prest] Two rings are elementarily equivalent if and only if they satisfy the same sentences in the language of rings. To some extent this is reflected in the representation theories of the two rings (one may see both positive and negative results along these lines in [5]). Here we concentrate on the case of a ring S and an elementary subring R of S. We show that if R is an elementary subring of S then the lattice of pp formulas for R-modules embeds in that for S-modules. These lattices, moreover, have the same finite sub-posets. From this we derive some corollaries. Then we consider to what extent the compositions of induction and restriction between R- and S-modules preserve elementary equivalence. Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 439-450 0022-4812 63:2<439 1998 63 JSL https://doi.org/10.2307/2586842 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586842 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Prest Mike Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK, E-mail: mprest@ma.man.ac.uk NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 439-450 0022-4812 63:2<439 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge