Premium
Representation extensions and amalgamation bases in rings
Author(s) -
Shoji Kunitaka
Publication year - 1994
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007464
Subject(s) - mathematics , injective function , ring (chemistry) , noncommutative ring , noetherian ring , pure mathematics , commutative ring , class (philosophy) , property (philosophy) , extension (predicate logic) , base (topology) , representation (politics) , noetherian , commutative property , algebra over a field , discrete mathematics , mathematical analysis , computer science , law , philosophy , chemistry , organic chemistry , epistemology , artificial intelligence , politics , political science , programming language
The main purposes of this paper are to investigate ℤ‐injective rings with the representation extension property and its dual, to give a necessary and sufficient condition for a ℤ‐injective ring to be an amalgamation base in the class of all rings and to determine structure of ℤ‐injective Noetherian rings which are amalgamation bases. Further, in the class of all commutative rings, it is shown that a commutative ring has the representation extension property, if, and only if, it is an amalgamation base.