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feat: tensor algebra of free module over integral domain is a domain (#…
…9890) Provide instances * `Nontrivial (TensorAlgebra R M)` when `M` is a module over a nontrivial semiring `R` * `NoZeroDivisors (FreeAlgebra R X)` when `R` is a commutative semiring with no zero-divisors and `X` any type * `IsDomain (FreeAlgebra R X)` when `R` is an integral domain and `X` is any type * `TwoUniqueProds (FreeMonoid X)` where `X` is any type (this provides `NoZeroDivisors (MonoidAlgebra R (FreeMonoid X))` when `R` is a semiring and `X` any type, via `TwoUniqueProds.toUniqueProds` and `MonoidAlgebra.instNoZeroDivisorsOfUniqueProds`) * `NoZeroDivisors (TensorAlgebra R M)` when `M` is a free module over a commutative semiring `R` with no zero-divisors * `IsDomain (TensorAlgebra R M)` when `M` is a free module over an integral domain `R` In Algebra.Group.UniqueProds: * Rename `UniqueProds.mulHom_image_of_injective` to `UniqueProds.of_injective_mulHom`. * New lemmas `UniqueMul.of_mulHom_image`, `UniqueProds.of_mulHom`, `TwoUniqueProds.of_mulHom` show the relevant property holds in the domain of a multiplicative homomorphism if it holds in the codomain, under a certain hypothesis on the homomorphism. Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
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