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The description of commutative subrings and commutative subalgebras and of the ideals innon-commutative rings and algebras are important directions of investigation for any class ofnon-commutative algebras or rings, because it allows one to relate representation theory, non-commutative properties, graded structures, ideals and subalgebras, homological and other prop-erties of non-commutative algebras to spectral theory, duality, algebraic geometry and topology naturally associated with the commutative subalgebras.
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