Solutions to exercises from *Introduction to Semigroups* by Petrich.

- Chapter 1: Preliminaries
- Chapter 2: Semilattice Decompositions
- Chapter 3: Ideal Extensions
- Chapter 4: Completely Regular Semigroups
- Chapter 5: The Translational Hull

## Solutions

- Chapter 1: Preliminaries
- Chapter 2: Semilattice Decompositions
- §2.1: Subdirect Products
- (II.1.5) (II.1.6) (II.1.7) (#1) (#2) (#3) (#4) (#5) (#6)
- §2.2: Completely Prime Ideals and Filters
- (II.2.3) (II.2.15) (II.2.17) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8)
- §2.3: Completely Semiprime Ideals and -Subsets
- (II.3.9) (II.3.13) (II.3.14) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9)
- §2.4: Semilattices of Simple Semigroups
- (II.4.4) (II.4.8) (II.4.10) (II.4.11) (II.4.12) (#1) (#2) (#3) (#4) (#5) (#6) (#7)
- §2.5: Weakly Commutative Semigroups
- (II.5.4) (#1) (#2) (#3) (#4) (#5) (#6)
- §2.6: Separative Semigroups
- (II.6.5) (II.6.7) (#1) (#2) (#3) (#4)
- §2.7: -Semigroups
- (II.7.6) (#1) (#2) (#3) (#4) (#5) (#6) (#7)

- Chapter 3: Ideal Extensions
- §3.1: Extensions and Translations
- (III.1.7) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9)
- §3.2: Extensions of a Weakly Reductive Semigroup
- (#1) (#2) (#3) (#4) (#5)
- §3.3: Strict and Pure Extensions
- (#1) (#2) (#3)
- §3.4: Retract Extensions
- (III.4.2) (III.4.6) (#1) (#2) (#3) (#4) (#5) (#6) (#7)
- §3.5: Dense Extensions
- (III.5.3) (III.5.10) (III.5.18) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8)
- §3.6: Extensions of an Arbitrary Semigroup
- (III.6.4) (III.6.11) (#1) (#2) (#3) (#4)
- §3.7: Semilattice Compositions
- (III.7.7) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10) (#11)

- Chapter 4: Completely Regular Semigroups
- §4.1: Generalities
- (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10)
- §4.2: Completely Simple Semigroups
- (IV.2.9) (#1) (#2) (#3) (#4)
- §4.3: Semilattices of Rectangular Groups
- (IV.3.5) (IV.3.6) (IV.3.11) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9)
- §4.4: Strong Semilattices of Completely Simple Semigroups
- (IV.4.7) (IV.4.8) (#1) (#2) (#3) (#4) (#5) (#6) (#7)
- §4.5: Subdirect Products of a Semilattice and a Completely Simple Semigroup
- (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10) (#11) (#12) (#13) (#14)

- Chapter 5: The Translational Hull
- §5.1: General Properties
- (V.1.2) (V.1.4) (V.1.8) (V.1.15) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10) (#11) (#12) (#13)
- §5.2: Isomorphisms and Automorphisms
- (#1) (#2) (#3)
- §5.3: Rees Matrix Semigroups
- (V.3.15) (#1) (#2) (#3) (#4) (#5) (#6)
- §5.4: Inverse Semigroups
- (V.4.2) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10) (#11) (#12)
- §5.5: Brandt Semigroups
- (V.5.5) (#1) (#2) (#3) (#4) (#5)
- §5.6: Semilattices of Groups
- (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9)