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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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Completed tensor product and power series rings
I want to know if the notion of completed tensor product in Stacks Project Tag 0AMU is the one that yields
$$k[[x]] \widehat{\otimes} k[[y]]≅k[[x,y]].$$
Here I should be considering the inverse limit …