| 21. | A ring homomorphism between the same ring is called an endomorphism and an isomorphism between the same ring an automorphism.
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| 22. | ;"'endomorphism ring "': A ring formed by the endomorphisms of an algebraic structure.
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| 23. | In the case when the endomorphism ring, where each endomorphism arises as left multiplication by a fixed ring element.
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| 24. | In the case when the endomorphism ring, where each endomorphism arises as left multiplication by a fixed ring element.
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| 25. | The usual definition of the characteristic polynomial of an endomorphism A of a finite dimensional vector space uses the determinant.
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| 26. | As a more illuminating example, the classification of groupoids with one endomorphism does not reduce to purely group theoretic considerations.
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| 27. | In other words, there is a ring homomorphism from the field into the endomorphism ring of the group of vectors.
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| 28. | Every element of defines the adjoint endomorphism ( also written as ) of with the help of the Lie bracket, as
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| 29. | Suppose that the field has an endomorphism whose square is the Frobenius endomorphism : " ? " } }.
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| 30. | Suppose that the field has an endomorphism whose square is the Frobenius endomorphism : " ? " } }.
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