Very soon mcq and study material as per college cadre exam will be shared.
Simiarity and Difference between Group theory and Ring theory
At a very basic level, there are various concepts that are common or similar between groups and rings as well as many other algebraic categories: normal subgroups play a similar role to (two-sided) ideals, homomorphisms are maps which preserve structure, there are “neutral” elements, and so on.
But this doesn’t make Group Theory and Ring Theory similar, at all. They are profoundly different.
Finite group theory is a huge deal. Finite rings, not at all.
Commutative Algebra, which is the study of commutative rings, is a massive, massive theory. The theory of Abelian groups is far smaller, and generally far simpler. The emphasis in group theory is heavily skewed towards the non-commutative case, while for rings it’s the other way around (though less heavily).
The questions of group theory and ring theory are different. The methods are different. The answers are different. I honestly can’t think of any significant similarity between the two domains.
At a very basic level, there are various concepts that are common or similar between groups and rings as well as many other algebraic categories: normal subgroups play a similar role to (two-sided) ideals, homomorphisms are maps which preserve structure, there are “neutral” elements, and so on.
But this doesn’t make Group Theory and Ring Theory similar, at all. They are profoundly different.
Finite group theory is a huge deal. Finite rings, not at all.
Commutative Algebra, which is the study of commutative rings, is a massive, massive theory. The theory of Abelian groups is far smaller, and generally far simpler. The emphasis in group theory is heavily skewed towards the non-commutative case, while for rings it’s the other way around (though less heavily).
The questions of group theory and ring theory are different. The methods are different. The answers are different. I honestly can’t think of any significant similarity between the two domains.
Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function
Three famous inequalities of statistics
1. Jensen's inequality
2. Chebyshev inequality
3. Markov inequality
1. Jensen's inequality
2. Chebyshev inequality
3. Markov inequality
Do you know about even and odd numbers? if yes then try :
0.5 is an even number
0.5 is an even number
Anonymous Quiz
30%
True
70%
False
Simple module
In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero proper submodules.
In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero proper submodules.