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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

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Banach algebra $A$ without an approximate identity but $A^2=A$

Please help me with the following question. What are some examples of Banach algebra $A$ satisfying the following two conditions? $1$.$ A $ does not have an approximate identity. $2$. $A^2=A$. T …
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