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Let be a commutative field of characteristic and let , where and are two finite cyclic groups. We give some structure results of finitely generated -modules in the case where the order of is divisible by . Extensions of modules are also investigated. Based on these extensions and in the same previous case, we show that -modules satisfying some conditions have a fairly simple form.

Finitely Generated Modules over Group Rings of a Direct Product of Two Cyclic Groups