数学线性代数代写 Math 541代写 线性代数代写 数学作业代写
401Math 541 HW1 - Linear Algebra Refresher 数学线性代数代写 Remarks: A) Definition is just a definition, there is no need to justify or explain it. B) Answers to questions with proofs should b...
View detailsSearch the whole station
半群理论代写 Let S be a semigroup, and let e, z, u ∈ S. Then: (i) e is a left identity if ex = x for all x ∈ S; (ii) e is a right identity if xe = x for all x ∈ S
Let S be a semigroup, and let e, z, u ∈ S. Then:
(i) e is a left identity if ex = x for all x ∈ S;
(ii) e is a right identity if xe = x for all x ∈ S;
(iii) z is a left zero if zx = z for all x ∈ S;
(iv) z is a right zero if xz = z for all x ∈ S;
(v) z is a zero if it is both a left zero and a right zero;
(vi) e is an idempotent if e2 = e.
(a) Suppose that S has a left identity e and a right identity f. Show that e = f and S has a 2-sided identity.
(b) Prove that if S has a zero element, then it is unique.
(c) Is it true that if a semigroup S has left zero and right zero, then they are equal and S has a zero element?
1-2. Prove that the size of the full transformation semigroup Tn is nn.
1-3. Prove that a mapping f ∈ Tn is a right zero if and only if it is a constant mapping. Does Tn have left zeros? Does it have a zero? Does Tn have an identity?
rank(fg) ≤ min(rank(f),rank(g)).
Find examples which show that both the equality and the strict inequality may occur.
1-7. Let G be a group and let a ∈ G. Then define
aG = { ag : g ∈ G } and Ga = { ga : g ∈ G }.
Prove that aG = Ga = G for all a ∈ G.
1-8.* Let S be a non-empty semigroup such that aS = Sa = S for all a ∈ S.
(a) If b ∈ S is arbitrary, then prove that there exists an element e ∈ S such that be = b.
(b) Prove that e is a right identity for S.
(c) In a similar way prove that S has a left identity too. Conclude that S is a monoid.
(d) Prove that S is a group.
更多代写:C#澳洲代写被抓 gmat online代考 英国网上考试怎么监考 分析论文格式怎么写 assignment写作技巧 流体动力学作业代写
合作平台:essay代写 论文代写 写手招聘 英国留学生代写
Math 541 HW1 - Linear Algebra Refresher 数学线性代数代写 Remarks: A) Definition is just a definition, there is no need to justify or explain it. B) Answers to questions with proofs should b...
View detailsMATH 5735 - Modules and Representation Theory Assignment 1 模块和表示论代写 1. (9 marks) Recall that an integral domain is a commutative ring (with unity) that has no zero divisors. (a) Pro...
View detailsMT4514 Graph Theory Assignment 1 图论代写 This assignment forms 5% of the assessment for this module. The assignment will be marked out of 20 marks. Please answer all questions, This assi...
View detailsMth 440/540 Homework 计算数论作业代写 (1) Part I a.) Use Mathematica to determine the 100th prime, the 1000th prime, and the 10,000th prime. b.) Use Mathematica to determine the prime (1) ...
View details