6 Answered Questions for the topic Groups

principal ideal ring

Suppose thatR=R1⊕R2⊕…….⊕Rnwhere each Ri is a principal ideal ring. Verify that R is also a principal ideal ring.   please I want help with that  

show that R x Zn has an identity element.

Suppose that R is a ring of characteristic n. If addition and multiplication are defined in R x Zn = {(x, a)lx E R; a E Zn} by (x, a) + (y, b) = (x + y, a +n b), (x, a)(y, b) = (xy + ay + bx,... more

Ideal and subring

please I want help with that     Consider the ring Mn(R) ofn x n matrices over R, a ring with identity. A square matrix (aij) is said to be upper triangular if aij = 0 for i > j and strictly... more


How do I calculate the number of protons and neutrons for a fictitious element when only given the atomic weight?

I have a list of fictitious elements to put into a periodic table (of my own design).  I have the atomic weight, physical state (gas, diatomic gas, hard brittle solid, ,hard w/high melting point,... more
Groups Math Maths


Group axioms proof

A group is a collection G that satisfies the following 3 axioms: 1) associativity a·(b·c)= (a·b)·c 2) identity element e: e·a=a ∀a in G 3) Inverse. Each element a in G has an inverse a-1 such that... more


Conjugacy classes of loop

If we consider the symmetry group H of rotations and reflections of 3 equidistant points on a circular loop then the group elemetns in cycle notation are:    e: (1)(2)(3) a: (123) b: (132) c:... more

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