a. Show that an intersection of subrings of a ring R is again a subring of R.
Question:
a. Show that an intersection of subrings of a ring R is again a subring of R.
b. Show that an intersection of subfields of a field F is again a subfield of F.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 81% (11 reviews)
a Let R be a ring and let H i R for i I Theorem 74 shows that H iI H i is an additive group Let a b ...View the full answer
Answered By
AJIN KURIAKOSE
I HAVE ELECTRONICS ENGINEERING DEGREE..AND MY AREA OF INTEREST IS MATHEMATICS,CONTROL SYSTEM,NETWORK,DIGITAL
4.70+
21+ Reviews
32+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Show that an intersection of ideals of a ring R is again an ideal of R.
-
Show that an intersection of subdomains of an integral domain D is again a subdomain of D.
-
Show that an intersection of normal subgroups of a group G is again a normal subgroup of G.
-
Several industries located along the Ohio River discharge a toxic substance called carbon tetrachloride into the river. The state Environmental Protection Agency monitors the amount of carbon...
-
What is the difference between graphing a relationship as we did in Chapter 2 and graphing a frequency distribution?
-
If f and t are the functions whose graphs are shown, let P(x) = f (x) t(x), Q(x) = f (x)/t(x), and C(x) = f (g(x)). Find (a) P'(2), (b) Q'(2), and (c) C'(2). - 1
-
You are given three bars of metal. Two of them are magnets, and the third is made of a magnetic material but is not magnetized. Describe how, using only the three bars, you could determine which of...
-
Sams Subs purchased a delivery van on January 1, 2014, for $35,000. In addition, Sams paidsales tax and title fees of $1,500 for the van. The van is expected to have a four-year life and a salvage...
-
6. The number of (staircase) paths in the xy-plane from (0, 0) to (7, 5) where each such path is made up of individual steps going one unit upward (U) or one unit to the right (R). (a) 12C5 (b) 12!...
-
A company has decided to order 360 units whenever the on-hand inventory falls to 90 units. There appears to be no seasonal fluctuation to the demand, but it does fluctuate daily and is approximately...
-
Let R be a ring, and let a be a fixed element of R. Let R a be the subring of R that is the intersection of all subrings of R containing a. The ring R a is the subring of R generated by a. Show that...
-
Show that a subset S of a ring R gives a subring of R if and only if the following hold: 0 S; (a - b) S for all a, b S; ab S for all a,b S.
-
Define what is meant by short-sea shipping (SSS), and discuss some advantages of SSS.
-
ELMI Corporation acquired a barn and three acres of land for a lump-sum price of $2,400,000. The barn contained used but fully-functional farming equipment. According to independent appraisals, the...
-
Ashleigh Batista is 42 years old and divorced. Her net income for 2023 is $84,400. She has retained the family home and custody of both children, who live with her. Her son is 23 years old, has no...
-
One of the 5 major tax issues associated with mergers, acquisitions and divestitures is whether the acquirer uses cash from newly issued equity or cash from retained earnings to purchase the target...
-
A taxpayer purchased used business equipment on November 20, 2016, for $100,000. The equipment was sold for $60,000 on August 25, 2018. Depreciation information is as follows: Accelerated...
-
The length of a picture is 5.25 inches shorter than twice the width. If the perimeter of the picture is 121.5 inches, find its dimensions. width length in in
-
The manager at Striker Corporation can hire only one student for the summer. She can hire Ken, a marketing student, who will do research on a marketing plan, or Lisa, a tax student, who will research...
-
Discuss the information available from the following techniques in the analysis of inorganic pigments used in antique oil paintings: (i) Powder X-ray diffraction, (ii) Infrared and Raman...
-
An antique collector is shipping $50,000 worth of items from Europe to America and must decide whether to insure the shipment for its full value. An insurance firm will provide this protection for a...
-
What is the most important difference between Bayesian and non-Bayesian decision criteria?
-
In Exercise 19.10, the probabilities for the three market conditions are estimated as 0.1, 0.6, and 0.3, respectively. Which design should be selected in order to maximize the firms expected profit?...
-
Why does seasonality of sales pose particular problems for companies preparing interim reports?
-
How do unmodified opinions and qualified opinions expressed in the auditor's report differ from one another?
-
Quality Suites Hotels includes the following selected accounts in its general ledger at December 3 1 , 2 0 2 5 : View the accounts. Prepare the liabilities section of Quality Suites Hotels' balance...
Study smarter with the SolutionInn App