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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

What does the sum of a number and its cubed look like if its turned into verbal expression?

We did not find results for: We did not find results for: 8 x − 27 ≤ − x 18 Answer is 5 and all numbers less than that. Explanation: This is just mostly interpretation, so to do this, we know 8 times a number is 8x, therefore it's 8x. Minus twenty-seven is subtracting 27, so 8 x − 27 . "No more than" means nothing more, but it can be less so ≤ (that means less than or equal to which means the number on the right has to be greater than the number on the left or it can be equal to it). Negative of that number means − x because we don't know what "that number" is so we can assume it's x. Plus 18 means...plus 18? So you can do − x 18 . To solve this, you can add 27 on both sides and also add x to both sides to get: 9 x ≤ 45 Then divide both sides by 9 to get x ≤ 5 . Therefore from interpretation, you can say that the answer is 5 and all numbers less than that works.. Check spelling or type a new query..

What is a theorem of group theory?

Group theory has many theorems, most of which wouldn't be interesting unless you familiarized yourself with the subject!

Here is one: If H is a subgroup of G, the number of elments in H must divide the number of elements in G.

What is physical interpretation of vector space?

A vector has two properties: magnitude and direction. The representation of a vector is an arrow. The tip of the arrow points to the direction the vector is acting. The length of the arrow represents the magnitude.

What exactly is algebra?

it is just simplification of a complex mathematical equation..

Why algebra not pointless?

Look at the example problems in any algebra book. Though some of the examples may be a bit far-fetched, many of the examples are similar to problems that scientists and engineers need to solve in the real world.

How do you solve gram to milligram?

1 gram = 1,000 milligrams.

So multiply the number of grams by 1,000.

What connection are their between nurse and algebra 1?

there both porn stars the answerer has just answered your restarted question

What is the value of a 1921silver dollar?

Please see the link below

Also, this site has a Coins and Currency thread that is more appropriate to questions about, uh, coins and currency. Money and Credit is generally for questions about credit cards, finances, checking accounts, etc.

What is the other point on the graph if y equals 2 and the slope is 0?

There are infinitely many points on the line and so it is not clear what you mean by "the other".

What are all the negative non integers that have a product of 20?

There are infinite number of negative non integers that have a product of 20. Any two negative fractions can make a product of 20. e.g.

-3/20 * -800/6 = 20

-3/8 * -320/6 = 20

-9/7 * -140/9 = 20

The list is endless. Only make sure you select both negative fractions to get a positive 20 and when selecting the fractions the numerator of one number is divisible by the other number's denominator such that the factors cancel to give 20.

What is Phi and give its concept and how to work out algebraically?

Phi is the Golden ratio.

It is a way of dividing a rectangle such that the ratio of the two sides of the whole rectangle are the same as the ratio of the sides of the smaller rectangle.

Using measurement units such that the small rectangle is 1*f, therefore the larger one is f*(f+1). f is actually phi, but this browser is not so good for Greek letters.

Equality of the ratios imply that 1/f = f/(f+1)

Cross-multiplying, f2 = f + 1

therefore f2 - f - 1 = 0

Using the quadratic formula, f = [1 + sqrt(1 + 4)]/2 - the other root is negative and so not appropriate for a length.

Therefore phi = f = [1 + sqrt(5)]/2 = 1.61803 (approx).

What is the value of a 40-44 model 1873 serial number 220347B?

Impossible to answer without knowing who made it and a detailed description of every aspect of the weapon

What is indepenedent variable?

an independent variable will not change with the amount of matter present. Think of it as being independent of the amount of material that is there