What is a generating set in abstract algebra? A Generating Set In this question we define the concept of a generating set which arise in the definitions of algebraic structures such as Groups, Rings, Fields and Vector Spaces. Generating sets play an important role in the concepts of cyclic al...
I just finished a section of a course that touched on the spectra Spec(R)Spec(R) of commutative rings RR, first as sets, then as topological spaces, and finally as locally ringed spaces. (I understand that elsewhere this is called the structure sheaf on Spec(R)Spec(R))...
People often think that “algebra” sounds like a big and scary thing, but I think that’s mostly just because they don’t understand what it actually is. Which is a real shame because algebra is incredibly useful in the real world. Plus, it turns out that the big ideas behind it all...
Another example of a concept in the field of abstract algebra would be finding the different possible arrangements of a Rubik's Cube, which would create a (large) group. Modern algebra, another term for abstract algebra, is a mathematical branch that explores the general algebraic structure of ...
I don't think I understand the construction of your ring, but it is well known that every boolean ring can be turned into a boolean algebra. To (hopefully) answer your question, we can set $$\overline{x} = x+1$$ Then $$\overline{x}y + x\overline{y} = (x+1)y + ...
Classical algebra is a term used to describe algebra as most people know it, which is an area of algebra that focuses on finding values for unknown... See full answer below. Learn more about this topic: Algebra Terms & Vocabulary
The field of algebra can be further broken into basic concepts known as elementary algebra or the more abstract study of numbers and equations known as abstract algebra, where the former is used in most mathematics, science, economics, medicine, and engineering while the latter is mostly used on...
A central idea of each chapter was the way that preservice teachers' learning of abstract algebra could both reinforce and build on their knowledge of secondary mathematics. We focus our commentary primarily on this idea. First, we will characterize the possible benefits of this bidirectional ...
A disaster is defined as a sudden, destructive occurrence that disrupts a community's or society's functioning and causes human, environmental damage, economic and material losses. It is greater than the community's or society's capacity to cope with using its resources. While often caused by ...
Why don’t we teach our younger mathematicians the bits and pieces ofreal, beautiful, and abstractmathematics that makes the field so supremelycool?In other words, why don’t we teach the mathematical versions of “Mary had a little lamb”? To be honest, I don’t know why we don’t. ...