caa a22 4500 386385874 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001377 doi S0305004100001377 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001377 Sharp R. Y. Department of Pure Mathematics, The University, Sheffield S3 7RH Certain countably generated big Cohen-Macaulay modules are balanced [Elektronische Daten] [R. Y. Sharp] Throughout this note, A will denote a (commutative, Noetherian) local ring (with identity) having maximal ideal m and dimension d. Let x1, ..., xd be a system of parameters (s.o.p.) for A. A (not necessarily finitely generated) A-module M is said to be a big Cohen-Macaulay A-module with respect to x1, ..., xd, if x1, ..., xd is an M-sequence. In the last ten or fifteen years there has been substantial interest in such modules, initially stemming from M. Hochster's discoveries that, if A contains a field as a subring, and x1, ...,xd is any s.o.p. for A, then there exists a big Cohen-Macaulay A-module with respect to x1, ...,xd, and that the existence of such modules has important consequences for the local homological conjectures in commutative algebra: see [6]. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 73-77 0305-0041 105:1<73 1989 105 PSP https://doi.org/10.1017/S0305004100001377 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001377 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sharp R. Y. Department of Pure Mathematics, The University, Sheffield S3 7RH NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 73-77 0305-0041 105:1<73 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge