| 1. | Suppose that " I " is a non-zero left ideal contained in.
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| 2. | Replacing " right ideal " with " left ideal " yields an equivalent definition.
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| 3. | It contains the peak algebra as a left ideal.
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| 4. | Right ideals, left ideals, and two-sided ideals other than these are called " nontrivial ".
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| 5. | The left ideal has non-zero intersection with any non-zero left ideal of " R ".
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| 6. | It is not hard to show that every left ideal in takes the following form:
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| 7. | The left ideal has non-zero intersection with any non-zero left ideal of " R ".
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| 8. | This condition ensures that the algebra has a minimal nonzero left ideal, which simplifies certain arguments.
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| 9. | In 1947 Marcel Riesz constructed spinor spaces as elements of a minimal left ideal of Clifford algebras.
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| 10. | If " R " is a principal left ideal domain, then divisible modules coincide with injective modules.
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