If (R, +, ) is a ring, prove that C = |r R|ar = ra, for

Question:

If (R, +, •) is a ring, prove that C = |r ∈ R|ar = ra, for all a ∈ R] is a subring of R. (The subring C is called the center of R.)

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 09:03 AM

See More Questions

Determine whether each of the following statements is true or false. For each false statement give a counterexample. (a) If (/?, +, ) is a ring, and 0 S R with S closed under + and , then S is a...
Complete the proofs of Theorem 17.1 and Corollary 17.1. Let R[x] be a polynomial ring. a) If R is commutative, then R [x] is commutative. b) If R is a ring with unity, then R[x] is a ring with unity....
If R, 5, and T are rings and f:R S, g: S T are ring homomorphisms, prove that the composite function g o f: R T is a ring homomorphism.
Joan has been a full-time director of Sunnybank Pursuits Ltd (a trading company) since 2001 and has owned 10% of the company's ordinary shares since 2002. She retired in February 2021 and gave all of...
What abilities make a candidate more likely to succeed in an assignment as an expatriate? Which of these abilities do you have? How might a person acquire these abilities?
Outline the distinctive accounting features of partnerships and limited companies. L01
A manufacturing statement (a) computes cost of goods manufactured for the period, (b) computes cost of goods sold for the period, or (c) reports operating expenses incurred for the period.
Ben Reese is a painter for a small manufacturing plant. Sometimes he works directly on the product and sometimes he performs routine maintenance on the plants three buildings. He is paid $11.50 an...
Prepare journal entries to record the following merchandising transactions of Lowe's, which uses the perpetual Inventory system and the gross method. Hint. It will help to identify each receivable...
Magna Charter is a new corporation formed by Agnes Magna to provide an executive flying service for the southeastern United States. The founder thinks there will be a ready demand from businesses...
With C the field of complex numbers and S the ring of 2 Ã 2 real matrices of the form define f: C S by f(a + bi) = for a + bi C. Prove that f is a ring isomorphism. 8
Given a finite field F, let M2(F) denote the set of all 2 Ã 2 matrices with entries from F. As in Example 14.2, (M2(F), +, ¢) becomes a noncommutative ring with unity. a) Determine the...
Facilitated transport consider here the transport of a solute S across a homogeneous membrane from one external solution to another as a complex CS with a carrier C unable to leave the membrane...
The equation for the standard normal curve (the normal curve with mean 0 and standard deviation 1) graphs as an exponential curve. Graph this curve, whose equation is \[y=\frac{e^{-x^{2} /...
Design an undirected network with N=7 and L=12. Based on how you drew your network, classify it as either fully connected ,random, or scale-free. Justify your decision with a short paragraph response.
Use the Ch08_AviaCo database shown in Figure P8.35 to work Problems 3546. Modify the MODEL table to add the attribute and insert the values shown in the following table. Table P8.35 Attribute and...
The Tip Calculator app does not need a Button to perform its calculations. Reimplement this app to use property listeners to perform the calculations whenever the user modifies the bill amount or...
A particle, carrying a positive charge of $4 \mathrm{nC}$, located at $(5 \mathrm{~cm}, 0)$ on the $x$-axis experiences an attractive force of magnitude 115.2 $\mathrm{N}$ due to an unknown...
What has been the outcome of attempts to abolish or limit plea bargaining?
Orange juice producers are dismayed and puzzled. An economist told them that the reason the demand for orange juice fell is that a new technology allow tomato producers to pick ripe tomatoes more...
By how much does the ball in Example B clear a 10 ft fence that is 365 ft away if the wind is blowing directly from the fence toward Carolina at 8 mi/h?
Gonzo, the human cannonball, is fired out of a cannon 10 ft above the ground at a speed of 40 ft/s. The cannon is tilted at an angle of 60°. His net hangs 5 ft above the ground. Where does his...
Find the length of side AC 85.4 50.6
Use the failure probability and consequence scores shown in the table to determine the risk factor for the project. Maturity 0.2 Cost 0.5 Complexity 0.5 Schedule 0.1 Dependency 0.4 Reliability 0.2...
Heidi, age 61, has contributed $20,000 in total to her Roth 401(k) account over a six-year period. When her account was worth $50,000 and Heidi was in desperate need of cash, Heidi received a $30,000...
The liability for preferred dividends declared is recorded on the date of record. 1 point True False

If (R, +, ) is a ring, prove that C = |r R|ar = ra, for

Question:

Step by Step Answer:

Since az z za for all a R we have z C and ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions