TY - JOUR
T1 - Differential projective modules over differential rings
AU - Juan, Lourdes
AU - Magid, Andy
N1 - Publisher Copyright:
© 2019, © 2019 Taylor & Francis Group, LLC.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/10/3
Y1 - 2019/10/3
N2 - Differential modules over a commutative differential ring which are projective as ring modules, with differential homomorphisms, form an additive category. Every projective ring module is shown occurs as the underlying module of a differential module. Differential modules, projective as ring modules, are shown to be direct summands of differential modules free as ring modules; those which are differential direct summands of differential direct sums of the ring being induced from the subring of constants. Every differential module finitely generated and projective as a ring module is shown to have this form after a faithfully flat finitely presented differential extension of the base.
AB - Differential modules over a commutative differential ring which are projective as ring modules, with differential homomorphisms, form an additive category. Every projective ring module is shown occurs as the underlying module of a differential module. Differential modules, projective as ring modules, are shown to be direct summands of differential modules free as ring modules; those which are differential direct summands of differential direct sums of the ring being induced from the subring of constants. Every differential module finitely generated and projective as a ring module is shown to have this form after a faithfully flat finitely presented differential extension of the base.
KW - Commutative rings
KW - differential algebra
KW - projective modules
UR - http://www.scopus.com/inward/record.url?scp=85064681107&partnerID=8YFLogxK
U2 - 10.1080/00927872.2019.1588975
DO - 10.1080/00927872.2019.1588975
M3 - Article
AN - SCOPUS:85064681107
VL - 47
SP - 4336
EP - 4346
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 10
ER -