ON n-SEMIHEREDITARY AND n-COHERENT RINGS

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International Electronic Journal of Algebra
Volume:1 Issue:1
ON n-SEMIHEREDITARY AND n-COHERENT RINGS

ON n-SEMIHEREDITARY AND n-COHERENT RINGS

Authors : Xiaoxiang Zhang, Jianlong Chen

Pages : 1-10

View : 39 | Download : 12

Publication Date : 2007-06-01

Article Type : Research Paper

Abstract :Let R be a ring. For a fixed positive integer n, R is said to be left n-semihereditary in case every n-generated left ideal is projective. R is said to be weakly n-semihereditary if each n-generated left insert ignore into journalissuearticles values(and/or right); ideal is flat. Some properties of n-semihereditary rings, respectively, weakly n-semihereditary rings and n-coherent rings are investigated. It is also proved that R is left n-semihereditary if and only if it is left n-coherent and weakly n-semihereditary, if and only if the ring of n × n matrices over R is left 1- semihereditary if and only if the class of all n-flat right R-modules form the torsion-free class of a torsion theory. Some known results are extended or obtained as corollaries
Keywords : weakly, n semihereditary ring, n coherent ring

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