Let R be a ring and G a group. An R-module A is said to be Artinian-by-(finite rank) if Tor_R(A) is Artinian and A/ Tor_R(A) has finite R-rank. We study a module A over a group ring RG such that A/C_A(H) is Artinian-by-(finite rank) (as an R-module) for every proper subgroup H.
KURDACHENKO, LEONID ANDREEVICH; SUBBOTIN, IGOR YAKOV; and CHUPORDYA, VASILIY ANATOLIEVICH
"On the structure of some modules over generalized soluble groups,"
Turkish Journal of Mathematics: Vol. 38:
1, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss1/6