caa a22 4500 477094775 CHVBK 20180405111524.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF03322197 doi (NATIONALLICENCE)springer-10.1007/BF03322197 A commutativity theorem for division rings and an extension of a result of Faith [Elektronische Daten] [Jairo Gonçalves, Arnaldo Mandel] It is shown that if a division ring is such that for every element a there exist co-monic integer polynomials f a , G a of different orders so that f a (a)/G a (a) is central then the ring is commutative. We extend this result to reduced PI rings, and show that it breaks down slightly for primitive rings, where the exceptions are characterized. This extends some earlier theorems of Herstein and Faith. Birkhäuser Verlag, Basel, 1996 primary 16U80 nationallicence secondary 16N80 nationallicence 16K99 nationallicence 16R40 nationallicence commutativity nationallicence division rings nationallicence PI rings nationallicence Gonçalves Jairo Dept. of Mathematics, Univ. of São Paulo, — Ag. Iguatemi, C.P. 66.281, 05389-970, São Paulo, SP, Brazil aut Mandel Arnaldo Dept. of Mathematics, Univ. of São Paulo, — Ag. Iguatemi, C.P. 66.281, 05389-970, São Paulo, SP, Brazil aut Results in Mathematics Birkhäuser-Verlag 30/3-4(1996-11-01), 302-309 0378-6218 30:3-4<302 1996 30 25 https://doi.org/10.1007/BF03322197 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF03322197 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gonçalves Jairo Dept. of Mathematics, Univ. of São Paulo, — Ag. Iguatemi, C.P. 66.281, 05389-970, São Paulo, SP, Brazil aut NATIONALLICENCE 700 1- Mandel Arnaldo Dept. of Mathematics, Univ. of São Paulo, — Ag. Iguatemi, C.P. 66.281, 05389-970, São Paulo, SP, Brazil aut NATIONALLICENCE 773 0- Results in Mathematics Birkhäuser-Verlag 30/3-4(1996-11-01), 302-309 0378-6218 30:3-4<302 1996 30 25 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer