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- W4313362741 abstract "In [28], for any real non associative algebra of dimension (mgeq2), having (k) linearly independent nilpotent elements (n_{1}), (n_{2}), …, (n_{k},) (1leq kleq m-1), Mencinger and Zalar defined near idempotents and near nilpotents associated to (n_{1}), (n_{2}), …, (n_{k}). Assuming (mathcal{N}_{k}mathcal{N}_{k}=left{ 0right}), where (mathcal{N} _{k}=operatorname*{span}left{ n_{1},n_{2},ldots,n_{k}right} ), they showed that if there exists a near idempotent or a near nilpotent, called (u), associated to (n_{1},n_{2},ldots,n_{k}) verifying (n_{i}uinmathbb{R}n_{i},) for (1leq ileq k), then any nilpotent element in (mathcal{N}_{k}) is unstable. They also raised the question of extending their results to cases where (mathcal{N}_{k}mathcal{N}_{k}not =left{ 0right} ) with (mathcal{N}_{k}mathcal{N}_{k}subsetmathcal{N}_{k}mathcal{ })and to cases where (mathcal{N}_{k}mathcal{N}_{k} notsubset mathcal{N}_{k}.) In this paper, positive answers are emphasized and in some cases under the weaker conditions (n_{i}uinmathcal{N}_{k}). In addition, we characterize all such algebras in dimension 3." @default.
- W4313362741 created "2023-01-06" @default.
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- W4313362741 date "2022-12-30" @default.
- W4313362741 modified "2023-09-27" @default.
- W4313362741 title "On a generalization of some instability results for Riccati equations via nonassociative algebras" @default.
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- W4313362741 doi "https://doi.org/10.3336/gm.57.2.06" @default.
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