caa a22 4500 386385572 CHVBK 20180307112057.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S0305004100077811 doi S0305004100077811 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100077811 Pure ring extensions and self FP-injective rings [Elektronische Daten] In this paper we investigate the following problem: is a ring R right self FP-injective if it has the property that it is pure, as a right R-module, in every ring extension? The answer is ‘almost always'; for example it is ‘yes' when R is an algebra over a field or its additive group has no torsion. A counter-example is provided to show that the answer is ‘no' in general. Rings which are pure in all ring extensions were studied by Sabbagh in [4] where it is pointed out that existentially closed rings have this property. Therefore every ring embeds in such a ring. We will show that the weaker notion of being weakly linearly existentially closed is equivalent to self FP-injectivity. As a consequence we obtain that any ring embeds in a self FP-injective ring. Copyright © Cambridge Philosophical Society 1989 Menal P. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Vámos P. Department of Mathematics, University of Exeter, Exeter EX4 4QE Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/3(1989-05), 447-458 0305-0041 105:3<447 1989 105 PSP https://doi.org/10.1017/S0305004100077811 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100077811 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Menal P. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain NATIONALLICENCE 700 1- Vámos P. Department of Mathematics, University of Exeter, Exeter EX4 4QE NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/3(1989-05), 447-458 0305-0041 105:3<447 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge