Suppose $G$ is a group and $H$ is a subgroup of $G$. $Ha$ is a right coset of $H$ in $G$. According to the Dover Book of Abstract Algebra p. 127, "Every coset in $G$ is a subset of $G$." I understand that since $H$ is a subgroup, it is closed with respect to multiplication. But nothing guarantees...

By third Isomorphism theorem , $\mathbb R/2\mathbb Z \Big/\mathbb Z/2\mathbb Z \cong \mathbb R/\mathbb Z$ ; so can we conclude that set of all distinct cosets of $\mathbb Z$ in $\mathbb R$ is not in bijective correspondence with the set of all distinct cosets of $2\mathbb Z$ in $\mathbb R$ ?

Let's as an upvoted answer to the old thread and comments here suggest remove intersection it's used for questions from «why intersection of two ideals is an ideal» to «how to compute this area of intersection using integral»; as Najib Idrissi puts it I don't think there should be tags "in...

Someone recently created the tag morphisms-of-schemes. Do we really need a tag separate from schemes for this? Especially with schemes, these objects being very often "over" another scheme, ie. the object studied is the morphism $S \to S_0$ where $S_0$ is some fixed base scheme ($\operatorname{Sp...

art, really? What is it good for? Do we really need it?