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