then this function is the composite of `FreeAddSemigroup.of` and a unique semigroup homomorphism `FreeAddSemigroup.lift f : FreeAddSemigroup α→ₙ+ M`. A typical element of `FreeAddSemigroup α` is a nonempty formal sum of elements of `α`. Contributor kim-em Apr 5, 2025 Sugge...
Why does X (when undefined in calculus) = 0? For example, y = x - 2 comes out to be y = -2 due to replacing x = 0. Explain. Explain why the following ring homomorphisms cannot exist. phi: Q -> Z __Fill...
Explain why the following ring homomorphisms cannot exist. phi: Q -> Z How to prove polynomial is isomorphic? In this algebraic expression, what is 3 called: 6n + 3 How to denote subgroup in math? When is a sheaf reflexive? Prove or disprove: For all x in the quaternions \mathbb{H}...
We compared the segregation pattern of genome-wide single nucleotide polymorphism markers in two contrasting bi-parental pedigree populations, the S3 with even sex ratio and the S5 with a female biased sex ratio. With the segregation analysis and comparison between the two populations, we were able...
The former is generally used for functions (specifically homomorphisms in groups) and the latter for spherical polars. Although they both have other uses, and that is a pretty vague rule... 172.70.86.44 18:21, 16 March 2022 (UTC) the natural numbers under '<'[edit] What does this ...
Given an example of a non-abelian group with 12 elements. Let \rho be a homomorphism from a group G to G'. Prove that ker(\rho) is a subgroup of G Prove that a ring with a cyclic additive group must be commutative. Why is associativity and commutativity important?