Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. Mathematicians now present 'big algebras,' a two-way mathematical 'dictionary' ...

Elementary group theory, groups, cosets, normal subgroups, quotient groups, isomorphisms, homomorphisms, applications.

This is a preview. Log in through your library . Abstract Let k be a commutative ring with unit of characteristic $p > 0$ and let G = Spec(A) be an affine commutative ...

A study found that carbon emissions from chat-based generative AI can be six times higher when responding to complex prompts, like abstract algebra or philosophy, compared to simpler prompts, such as ...