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Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators. The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property.
Socratic is an education tech company that offers a mobile app for students. The app uses AI technology to help students with their homework by providing educational resources like videos, definitions, Q&A, links and more.
MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. [1] It is a part of the Stack Exchange Network, but distinct from math.stackexchange.com.
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Brainly is an education company based in Kraków, Poland, with headquarters in New York City.It is an AI-powered homework help platform targeting students and parents. As of November 2020, Brainly reported having 15 million daily active users, making it the world's most popular education app. [2] In 2024, FlexOS reported Brainly as the #1 Generative AI Tool in the education category and the #6 ...
We first define a free product of two algebras. Let A and B be algebras over a commutative ring R . Consider their tensor algebra , the direct sum of all possible finite tensor products of A , B ; explicitly, T = ⨁ n = 0 ∞ T n {\displaystyle T=\bigoplus _{n=0}^{\infty }T_{n}} where
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