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چکیده
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In this paper, we introduce and study the concept of generalized monoform modules (G − M modules, for short) which is a proper generalization of that of monoform modules. We present some of their examples, properties and characterizations. It is shown that over a commutative ring R, the properties monoform, small monoform, G − M, compressible, uniform and weakly co-Hopfian are all equivalent. Moreover, we demonstrate that a ring R is an injective semisimple ring iff any R-module is G − M. Further, we prove a similar theorem to Hilbert’s basis theorem for monoform, small monoform and G − M modules.
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