Definition of Irreducible Graded $Z_2$ Modules

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I am reading Dale. Husemoller's Fiber Bundles where he defines graded modules over a graded algebra as follows.enter image description here

Next, he talks about irreducible graded modules in the lines given below.enter image description here

Now, I don't get it, How can an Irreducible graded Module be defined as it should not have any submodules. But graded implies the existence of $M^0 , M^1$.

I think I may have misinterpreted something. Kindly help!.

regards