Let (A,*) be a semigroup. For every a and b in A, if a + b, then abb* a. Show that, For every t in A, t*t=t b. For every I and m in A, C. For every x, y, z in A, (Note that if a b = ba then it implies a = b) a. | ★m ★ 1 = 1 x*y* z = x * z

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let (A,*) be a semigroup. For every a and b in A, if ab, then a b*b* a. Show that,
For every t in A,
t*t=t
b. For every I and m in A,
C. For every x, y, z in A,
a.
1★m ★ 1 = 1
x*y* z=x* z
(Note that if a b = ba then it implies a = b)
Transcribed Image Text:Let (A,*) be a semigroup. For every a and b in A, if ab, then a b*b* a. Show that, For every t in A, t*t=t b. For every I and m in A, C. For every x, y, z in A, a. 1★m ★ 1 = 1 x*y* z=x* z (Note that if a b = ba then it implies a = b)
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