An abelian group is the same as a $\mathbb{Z}$-module if we let integers "multiply" group elements in the obvious way (repeated addition). $\endgroup$ – hardmath Commented May 2, 2014 at 0:02

Dec 14, 2015 · A module is an object. The modulus (not the module btw) is something associated to a complex number. The term "modular" on the other hand is unrelated to either of these, and is probably most commonly a property certain things can have, namely modular forms. $\endgroup$ –

Initially I thought, since a module is a set of vectors, M would be some vectors of length 1, because an ideal is a set containing polynomials. But that seems to be incorrect. linear-algebra

Feb 28, 2018 · 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 modulo 5. Also, what does t...

Sep 16, 2021 · What is the twisted module ? What is the mechanism happening here ? From The Stack project, the definition ...

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 (e.g. topological, geometric). On the other hand, sometimes you want to consider a special class of representations, and so you have to change you group ring to something better ...

Feb 4, 2012 · The name "module" was introduced by Dedekind in his work on ideals and number fields. You can find both his paper (in translation) and his explanation in Stillwell's translation of Dedekind's third exposition of the theory of ideals, "Theory of Algebraic Integers", Cambridge University Press, Cambridge, 1996. It's a very nice read, and it is ...

Nov 29, 2013 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Mar 15, 2024 · $\begingroup$ @RandyMarsh I'm asking about the meaning of module outside of the context of lattice-based PQC, as well as its relation to module-lattice-based PQC. I'll clarify question. $\endgroup$ – DannyNiu

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.