6 Answered Questions for the topic Groups

11/29/16

#### 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

09/29/16

#### 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,...
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09/29/16

#### 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...
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07/11/15

#### 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,...
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#### 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...
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#### 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:...
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