# Subdirectly Irreducible Semigroups

### Description

Definition 1.1. The ordered pair (S,*) is a semi-group iff S is a set and * is an associative binary operation (multiplication) on S. Notation. A semigroup (S,*) will ordinarily be referred to by the set S, with the multiplication understood. In other words, if (a,b)e SX , then *[(a,b)] = a*b = ab. The proof of the following proposition is found on p. 4 of Introduction to Semigroups, by Mario Petrich. Proposition 1.2. Every semigroup S satisfies the general associative law.

i, 83 leaves

### Creation Information

Winton, Richard Alan December 1978.

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• Winton, Richard Alan

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### Description

Definition 1.1. The ordered pair (S,*) is a semi-group iff S is a set and * is an associative binary operation (multiplication) on S. Notation. A semigroup (S,*) will ordinarily be referred to by the set S, with the multiplication understood. In other words, if (a,b)e SX , then *[(a,b)] = a*b = ab. The proof of the following proposition is found on p. 4 of Introduction to Semigroups, by Mario Petrich. Proposition 1.2. Every semigroup S satisfies the general associative law.

i, 83 leaves

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#### UNT Theses and Dissertations

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### Creation Date

• December 1978

### Added to The UNT Digital Library

• May 10, 2015, 6:16 a.m.

### Description Last Updated

• June 7, 2016, 1:12 p.m.

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