Question: 6.2.3. If p : R - S is a ring homomorphism and R has an identity element 1, show that e = o (1) satisfies

6.2.3. If p : R - S is a ring homomorphism and R
6.2.3. If p : R - S is a ring homomorphism and R has an identity element 1, show that e = o (1) satisfies e2 = e and ex = xe = exe for all x E (R)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

if do - a, + a2 - . . . (-1)*a, is divisible by 11. 33. Show that the number 7, 176,825,942, 116,027,211 is divisible by 9 but not divisible by 11. 34. Show that the number 9,897,654,527,609,805 is...

Q:

"Fortran, Algol and Lisp invented most programming language concepts 50 years ago; adding the concept of object-orientation suffices to explain all programming languages to date". To what extent is...

Q:

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Q:

6. List all the polynomials of degree 2 in Zz[x]. Which of these are equal as functions from Z2 to Zz? 7. Find two distinct cubic polynomials over Z2 that determine the same function from Zz to Z2....

Q:

Let R be a ring with identity. Show that R is not a free module on any set in the category of all R-modules (as defined in Exercise 2). Data from in exercise 2 Let R be any ring (possibly without...

Q:

Let R be any ring (possibly without identity) and Fa free R-module on the set X, with L : X F, as in Exercise 2. Show that L (X) is a set of generators of the R-module F. is commutative. Conclude...

Q:

6. (i) Show that $N=\{12, 14, 21\}$ generates $\mathbb{Z} $ as a $\mathbb{Z} $-module. [2 Marks] (ii) Decide whether or not a proper subset of $N$ from part (i) [3 Marks] generates $\mathbb{Z}$ as a...

Q:

6. (i) Show that $N=\{12,14,21\}$ generates $\mathbb{Z}$ as a $\mathbb{Z}$-module. [2 marks] (ii) Decide whether or not a proper subset of $N$ from part (i) [3 marks] generates $\mathbb{Z}$ as a...

Q:

6. (i) Show that $N=\{12,14,21\}$ generates $\mathbb{Z}$ as a $\mathbb{Z}$-module. [2 marks] (ii) Decide whether or not a proper subset of $N$ from part (i) [3 marks] generates $\mathbb{Z} $ as a...

Q:

6. (i) Show that $N=\{12,14,21\}$ generates $\mathbb{Z}$ as a $\mathbb{Z}$-module. [2 marks] (ii) Decide whether or not a proper subset of $N$ from part (i) [3 marks] generates $\mathbb{Z}$ as a...

Q:

Jupiter service company decides to increase the amount of the petty cash fund from 500 to 600 the journal entry must be made to debit the cash account and credit the petty cash account for 100 true...

Q:

As the first auditor of the Newberg Company you discover that the following entries have been made in the property, plant, and equipment account: You discover the following additional information: 1....

Q:

High Court Reviews IPART A Which TWO of the following best identify the central ideas of this text The nature of truth Justice and fair trial Growing up Mental illness and its relationship to crime...

Q:

The date of death for a widow was 2 0 2 1 . If the estate was valued at $ 2 , 1 7 7 , 0 0 0 and the estate was taxed at 4 0 percent, what was the heir s tax liability? Use Exhibit 1 9 - 6 for Estate...