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Abstract Algebra

Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.

1,849 Questions

Weathering and erosion?

To put is simply, weathering is breaking big rocks into small rocks. Erosion is moving those small rocks somewhere else - by wind, water or ice.

Is one ninth a perfect square?

dont think so

* * * * *

A perfect square is a term that is normally used to refer to squares of integers and, in that respect, 1/9 cannot be a perfect square.

However, it is the square of ± 1/3.

Anyone limitation of cristal field theory?

1. anionic ligands like OH- placed below H2O :NO explanation provided

2. no explanation of why the strong field ligands are strong ,for example , though NH3 is lower in dipole moment than H2O it is a strong ligand

How do we prove that a finite group G of order p prime is cyclic using Lagrange?

Lagrange theorem states that the order of any subgroup of a group G must divide order of the group G. If order p of the group G is prime the only divisors are 1 and p, therefore the only subgroups of G are {e} and G itself. Take any a not equal e. Then the set of all integer powers of a is by definition a cyclic subgroup of G, but the only subgroup of G with more then 1 element is G itself, therefore G is cyclic. QED.

How do you solve 5x plus 2x plus 5 plus 1 minus x equals 18?

The solution of this equation is the value of variable 'x' for which L.H.S.= R.H.S. The given equation is: 5x+2x+5+1-x=18

6x+6=18

Adding -6 on both sides, we get

6x=12

Dividing both sides by 6, we get

x=2

Solution is x = 2.

What is the value a 1940 quarter?

If well-worn, about $6 regardless of mint mark. If almost uncirculated, 1940 quarters from Philadelphia are worth around $10, S-mint (San Francisco) coins go for about $15, and D-mint (Denver) coins are about $30.

Divide 184 into two parts such that one third of one part may exceed one seventh of the other part by 4?

One part is 63.6 and the other part is 120.4 Let x be one part and y be the other part. (1/3)X = (1/7)Y + 4 ... one third of one part can exceed one-seventh of the other part by 4. X + Y = 184 So you have two equations and two unknowns: X + Y = 184 (1/3)X - (1/7)Y = 4 After rerranging and solving the simlutaneous equations, you get X = 63.6 and Y = 120.4

What is he slope of -8 and -9?

In order to calculate the slope, you need two points, each with two coordinates. That makes four numbers in all. There are only two in the question.

What is point of origin?

The middle point of a graph also known as (0,0)

How do you work out 3x-4y equals 25?

3X - 4Y = 25

- 4Y = - 3X + 25

Y = (3/4)X - 25/4

===============the line

To find intercepts for a two point graphing exercise/

Y = - 25/4

-----------zero out Y

(3/4)X - 25/4 = 0

(3/4)X = 25/4

X = 25/3

------------------

(25/3, 0) and (0, - 25/4)

------------------------------------------points to graph line

What is value of ranger 22 caliber model 34?

If it has a magazine that adds at least 100$ if its in 90%condition or better that will add a hefty premium.I would say in real life <not gun book value?> one in 50% conditon with a magazine would be worth around 300$ close to double that in pristine condition.

What is the value of a 12 gauge model 48 Sportsman?

Value always based on condition - Very Good would be about $300.00, Vent Rib would add adout 20%

How do you read numbers with commas?

Easy, the commas separate the numerical units. 1,000 is one thousand. 1,000,000 is one million and so on.

How do you solve y over 4 equals 10 over 8?

y/4 = 10/8

Multiply both sides by 4:-

y = 40/8

y = 5

What are examples of idempotent matrix?

An idempotent matrix ( A ) satisfies the property ( A^2 = A ). Examples include the zero matrix ( \begin{pmatrix} 0 & 0 \ 0 & 0 \end{pmatrix} ) and the identity matrix ( \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} ). Another example is the projection matrix ( \begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix} ), which projects vectors onto the x-axis. Any matrix that can be expressed as a projection operator onto a subspace is also idempotent.