Let R be a ring with identity and let S be a subring of R containing the identity. Prove that if m is a unit in S then u is a unit in R. Show by example that the converse is false.

Question

06-12-2019
Mathematics

contestada

Let R be a ring with identity and let S be a subring of R containing the identity. Prove that if m is a unit in S then u is a unit in R. Show by example that the converse is false.

Respuesta :

Otras preguntas

When 8 is added to the difference between nine times a number and 9, the result is greater than 14 added to 88 times the number. find all such numbers?

Which overall message does this political cartoon convey? advertising on buses will raise money for schools. advertising on buses should be targeted toward scho

A ball is rolled twice across the same level laboratory table and allowed to roll off the table and strike the floor. In each trial, the time it takes the ball

which is the soultion set of the inequaliies 15y-9<36

convert 9 4/6 into improper fraction

how can you preventivas injury chile cycling? A. pedal slowly. b) release so me oficial tiene aire from tiene tires. c) get yogur bicycle custom-fitted. d) Lean

Ice is to water as rock is to: lava, sand or oil

△MAH∼△WCF . What is the value of x?

he knew that somebody would take it upon himself to arrive late. which word is the indefinite pronoun?

Which expression has a value of 39?

EnriquePires EnriquePires · Answer 1 · 2019-12-11T00:04:49+01:00

Explanation:

Since m is a unit in S, then, there exists b ∈ S such that m*b = 1, where 1 is the identity. Since S is a subring of R we have that m ∈ R, and therefore b is also the multiplicative inverse of m in R. The converse isnt true.

The set of real numbers is a Ring with the standard sum and multiplication. Every real number different from 0 has a multiplicative inverse. For example, the inverse of 2 is 1/2. However, 2 is not a unit on the subring of Integers Z.