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On the flat length of injective modules
Author(s) -
Emmanouil Ioannis,
Talelli Olympia
Publication year - 2011
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdr014
Subject(s) - injective function , infimum and supremum , mathematics , ring (chemistry) , dimension (graph theory) , injective module , pure mathematics , order (exchange) , group (periodic table) , regular ring , combinatorics , discrete mathematics , von neumann regular ring , physics , chemistry , organic chemistry , finance , quantum mechanics , economics
In this paper, we use the notion of strict Mittag–Leffler modules, in order to study the flat length of injective modules over a ring R . We show that the supremum of these flat lengths is closely related to the invariants silp R and spli R , which were defined by Gedrich and Gruenberg, as well as to the finitistic dimension of R and the injective length of the regular module. We also examine the special case where R =ℤ G is the integral group ring of a group G .