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Exact(2)
Here is another example of an algebra.
One example of an algebra for this functor is (N, α), where α a, b) = a + b and α a, b) = a × b.
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An important example of a localizing algebra is any algebra containing a nonzero compact operator.
A simple example of a Lie algebra with undecidable word problem was given by Kukin [142].
We use the following example (I, a) of an algebra for F: I= [0,1], and a : FI → I is given by a inl(x)) =.5 x, and a inr(x)) =.5 x +.5.
An example of such an algebraic encoding is the Lindenbaum-Tarski algebra, a Boolean algebra corresponding to classical propositional logic.
An important example of a strongly compact algebra is the commutant of a compact operator with a dense range.
Haagerup, An example of a nonnuclear C∗-algebra, which has the metric approximation property, Invent.
The skew field of quaternions ℍ gives an example of a noncommutative Clifford algebra with minimal dimension.
An example of tropical algebra analysis and design of partially defect tolerant hexagonal systolic multiplier will be given, too.
This algebra was the first example appearing in the literature of an algebra which is not directly finite, that is, in which there are elements x, y for which x y = 1 but y x ≠ 1.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com