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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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Dimension of subalgebras of a matrix algebra
If $n$ is given and $A$ is a subalgebra of $M_n(\mathbb C)$, the algebra of $n \times n$ matrices with entries in the field of complex numbers, then what are the possible values of dimension of $A$ as …