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Strongly ( 𝒯 , n ) -coherent rings, ( 𝒯 , n ) -semihereditary rings and ( 𝒯 , n ) -regular rings

Zhanmin Zhu (2020)

Czechoslovak Mathematical Journal

Let 𝒯 be a weak torsion class of left R -modules and n a positive integer. A left R -module M is called ( 𝒯 , n ) -injective if Ext R n ( C , M ) = 0 for each ( 𝒯 , n + 1 ) -presented left R -module C ; a right R -module M is called ( 𝒯 , n ) -flat if Tor n R ( M , C ) = 0 for each ( 𝒯 , n + 1 ) -presented left R -module C ; a left R -module M is called ( 𝒯 , n ) -projective if Ext R n ( M , N ) = 0 for each ( 𝒯 , n ) -injective left R -module N ; the ring R is called strongly ( 𝒯 , n ) -coherent if whenever 0 K P C 0 is exact, where C is ( 𝒯 , n + 1 ) -presented and P is finitely generated projective, then K is ( 𝒯 , n ) -projective; the ring R is called ( 𝒯 , n ) -semihereditary...

Structure of central torsion Iwasawa modules

Susan Howson (2002)

Bulletin de la Société Mathématique de France

We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro- p , p -adic, Lie group containing no element of order p . The techniques employed follow classical methods used in the commutative case, but using Ore’s method of localisation. We then consider the properties of certain invariants which may prove useful in determining the structure of a module. Finally, we describe the case of pro- p subgroups of GL 2 ( p ) in detail and...

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