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A fuzzy sphere differs from an ordinary sphere because the algebra of functions on it is not commutative.
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A commutative superalgebra is one which satisfies a graded version of commutativity.
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In formal language theory, alternation is commutative and associative.
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The natural sum is associative and commutative: it is always greater or equal to the usual sum, but it may be greater.
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In contemporary usage, a field is always commutative.
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However, for matrices over a more general ring that are "not" commutative, such as the quaternions, they may not be equal.
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It is inherently non-unital (except in the case of only one element), associative and commutative.
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For this reason, ring addition is commutative in general.
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This identity holds for any matrices over a commutative ring, but not for all rings in general.
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It is straightforward to show that multiplication is associative and commutative (up to isomorphism), and distributive over addition.
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