Search the whole station

# 数学半群代写 半群理论课业代写 MT5863代写 半群理论代写

106

## Green’s relations again, Simple semigroups

### Green’s relations again数学半群代写

7-2. Let Dr be the D-class of the full transformation semigroup Tn (n r) consisting of all the mappings with rank r. How many L -classes, R-classes and H -classes does Dr contain? What is the size of Dr?

7-3. Prove that the H -class Hf of a mapping f Tn is a group if and only if rank(f) = rank(f2 ).

7-4.

(a) Prove that the monoid of all partial transformations Pn is regular.

(b) Prove that there is an injective homomorphism from Pn to Tn+1.

(c) Prove that the following hold in Pn:

7-5. Let S be a semigroup and let e S be an idempotent. Suppose that Le, Re and De are the L -, R-, and Dclass of e, respectively. Prove that LeRe = De.

7-6. Let a, b be elements in a D-class D. Show that ab Ra Lb if and only if Rb La contains an idempotent.

7-7. Show that if S is a periodic semigroup then a D-class D consists of regular elements if and only if there are a, b ∈ D such that ab ∈ D.

### Simple semigroups数学半群代写

7-8. Prove that a subsemigroup S of Tn is simple if and only if rank(f) = rank(g) for all f, g S.

7-9. Let S be a monogenic semigroup (which we recall means that there is s S such that S = ⟨s⟩). Prove that S is simple if and only if S is a group. What about if S = ⟨a, b, is it still true that S is simple if and only if S is a group?

7-10. Prove that in a finite simple semigroup S

ac = bc and ca = cb a = b

for any a, b, c S.

Is it true that

ac = bc ⇒ a = b

for any a, b, c ∈ S?

The prev: The next:

### Related recommendations

• #### 计算机体系结构cs代写 I218代写 计算机体系结构作业代写

69

I218 Computer ArchitectureReport 3 计算机体系结构cs代写 (1) In the textbook and lecture slides, detailed information in the pipeline registers (IF/ID, ID/EX, EX/MEM, MEM/WB) is not provided. ...

View details
• #### cs计算机体系结构作业代做 I218代写 计算机体系结构代写

65

I218 Computer ArchitectureReport 2 cs计算机体系结构作业代做 (1)How is the instruction “sub \$t9, \$s4, \$s7” translated to a machine instruction code? Answer the rs, rt, and rd fields in binary n...

View details
• #### 经济问题集代做 Economics 426代写 经济学作业代写代做

80

Economics 426: Problem Set 1 – Robinson Crusoe 经济问题集代做 I. Robin Crusoe is endowed with 112 labor-hours per week. There is a production function for the output of oysters Spring...

View details
• #### 经济学生产问题代写 Economics 426代写 经济学作业代写

75

Economics 426: Problem Set 8 – Production 经济学生产问题代写 I. Show that if A and B are closed subsets of Rn , then A+B is closed or provide a counter example. (20 pts) II. Show that if A and...

View details
1