Symplectic algebras and poisson algebras |
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| Authors: | Frank Loose |
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| Institution: | 1. Mathematisches Institut der Heinrich-Heine-Universit?t , Düsse;2. dorf Universit?tsstr 1 , D - 4000, Düsseldorf |
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| Abstract: | Abstract A ring R is called left P-injective if for every a ∈ R, aR = r(l(a)) where l( ? ) and r( ? ) denote left and right annihilators respectively. The ring R is called left GP-injective if for any 0 ≠ a ∈ R, there exists n > 0 such that a n ≠ 0 and a n R = r(l(a n )). As a response to an open question on GP -injective rings, an example of a left GP-injective ring which is not left P-injective is given. It is also proved here that a ring R is left FP -injective if and only if every matrix ring 𝕄 n (R) is left GP-injective. |
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| Keywords: | FP-injective ring GP-injective ring Matrix ring P-injective ring |
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