Strongly Goldie Dimension

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dc.creatorShen, Liang
dc.creatorChen, Jianlong
dc.date2005-10-09
dc.date.accessioned2026-07-07T06:47:16Z
dc.date.available2026-07-07T06:47:16Z
dc.descriptionLet $R$ be an associative ring with identity. A unital right $R$-module $M$ is called strongly finite dimensional if Sup$\{{\rm G.dim} (M/N) | N\leq M\} < +\infty$. Properties of strongly finite dimensional modules are explored. It is also proved that: (1)If $R$ is left $F$-injective and strongly right finite dimensional, then $R$ is left finite dimensional. (2) If $R$ is right $F$-injective, then $R$ is right finite dimensional if and only if $R$ is semilocal. Thus the Faith-Menal conjecture is true if $R$ is strongly right finite dimensional. Some known results are obtained as corollaries.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0510175
dc.identifierhttp://arxiv.org/abs/math/0510175
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103596
dc.subjectRings and Algebras
dc.subject16L60, 16D50
dc.titleStrongly Goldie Dimension
dc.typetext

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