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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.
1
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How much information does the multiplicative semigroup of an algebra contain?
What also came into my mind is, that from matrix algebras of the form $A \otimes M_2$ we can recover the addition from the multiplication:
$$\left (\begin{array} 11 & 1 \\ 0 & 0 \end{array} \right ) …
2
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How much information does the multiplicative semigroup of an algebra contain?
How much do we know about an given algebra when we only know its semigroup strucure under the product law?
How far can two algebras be distinguished by knowing only their semigroup strucure?
The sam …