| 1. | The endomorphism ring is simply the ring of formal power series.
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| 2. | Any such complex torus has the Gaussian integers as endomorphism ring.
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| 3. | Consequently, the endomorphism ring of any simple module is a division ring.
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| 4. | Square matrix rings arise as endomorphism rings of free modules with finite rank.
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| 5. | In particular, the endomorphism ring of a simple module is a division ring.
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| 6. | Endomorphism ring theorems and converses were investigated later by Mueller, Morita, Onodera and others.
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| 7. | Next, one notes that the set of endomorphisms of an abelian group is an endomorphism ring.
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| 8. | Thus the endomorphism ring of the module " M " is " as small as possible ".
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| 9. | ;"'endomorphism ring "': A ring formed by the endomorphisms of an algebraic structure.
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| 10. | In the case when the endomorphism ring, where each endomorphism arises as left multiplication by a fixed ring element.
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