IS:P

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
    (I.3.3) (I.3.5) (I.3.7) (I.3.9) (I.4.2) (I.4.5) (I.4.13) (I.5.5) (I.5.6) (I.5.8) (I.5.12) (I.5.14) (#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10) (#11) (#12) (#13) (#14) (#15) (#16) (#17) (#18) (#19) (#20) (#21) (#22) (#23) (#24) (#25) (#26)
  • 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 \mathfrak{N}-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: \mathfrak{N}-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)

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