Discrete Mathematics

-------------------------ALGEBRAIC

STRUCTURES

169

5.1.1

Types

of

Homomorphism

From algebra

A=

<k,

op

1

,

••••

,

op

11

> to algebra

Homomorphism

B

= <k', op'

1

,

••••

,

op'n>

Conditions

(i) endomorphism

(ii) epimorphosis

(iii) monomorphism

(iv) isomorphism

(v) automorphism

A=B

f:

k

~

k'

is onto

fis

one-to-one (injective)

f is one-to-one, onto (bijective)

A = B and f is an isomorphism.

Boolean algebra of sets Let

~

be

a collection

of

sets closed under union, intersection, and comple-

ment. Then

~

is a Boolean algebra, with the empty set

<1>

as the zero element and the universal set U as the unit

element.

Set

of

propositions

1t

as a Boolean algebra ...