May 1, 2014 · The definition of modules confuses me: $R$ is a ring, then a left $R$ module is an abelian group $V$ together with a multiplication map $$R \\times V \\to V, (r,v ...

So, I am trying to imagine what a Module and R-module look like, and what kind of elements are in these structures. For a Module, it's analogous to a ring of a vector space over a field. So …

Sep 1, 2020 · For example, even though module theory is well-suited for cohomological considerations, your group might have extra structure that is not encoded in your group ring …

If you assume a left R module is also a right R module then you will need commutativity of R in order for the last property to hold

Dec 3, 2024 · $5 \equiv 1 \pmod {2}$ This is typical notation for this equivalence relation on $\mathbb {Z}$. $5 = 1 \pmod {2}$ This is fairly common notation for the equivalence relation. …

Feb 4, 2012 · I know that a module is a generalization of a vector space, but I would like to know why are modules called modules? Thanks for your kindly help.

Jun 27, 2021 · In contrast, the word "module" never implies that the scalar ring is a field, because we have a specific term for that case: "vector space". Additionally, sometimes when people …

May 16, 2015 · I really can't get my head around this "modulo" thing. Can someone show me a general step-by-step procedure on how I would be able to find out the 5 modulo 10, or 10 …

May 31, 2015 · I want a book to cover the following topics in Module Theory: Modules, Submodules, Quotient modules, Morphisms Exact sequences, three lemma, four lemma, five …

May 17, 2021 · I have a curiosity question on a fundamental difference between vector spaces and general modules over rings. Some of the fundamental facts of linear algebra: (1) A finitely …