## Lattice Theory, Volume 25, Part 2Since its original publication in 1940, this book has been revised and modernized several times, most notably in 1948 (second edition) and in 1967 (third edition). The material is organized into four main parts: general notions and concepts of lattice theory (Chapters I-V), universal algebra (Chapters VI-VII), applications of lattice theory to various areas of mathematics (Chapters VIII-XII), and mathematical structures that can be developed using lattices (Chapters XIII-XVII). At the end of the book there is a list of 166 unsolved problems in lattice theory, many of which still remain open. It is excellent reading, and ... the best place to start when one wishes to explore some portion of lattice theory or to appreciate the general flavor of the field. --Bulletin of the AMS |

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it is a nice book which was studied by me. it covers all the topics of lattice theoretic many examples and so many excersizes

are given.it is useful for graduates and researchers .

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interesting to read and easy to understand

### Contents

1 | |

CHAPTER II | 20 |

CHAPTER III | 55 |

GEOMETRIC LATTICES | 80 |

COMPLETE LATTICES | 111 |

CHAPTER VI | 122 |

UNIVERSAL ALGEBRA | 132 |

APPLICATIONS TO ALGEBRA | 159 |

CHAPTER XI | 254 |

CHAPTER XII | 277 |

LATTICEORDERED GROUPS | 287 |

LATTICEORDERED MONOIDS | 319 |

CHAPTER XV | 347 |

POSITIVE LINEAR OPERATORS | 380 |

CHAPTER XVII | 397 |

411 | |

### Common terms and phrases

Archimedean automorphisms Banach lattice binary operation Boolean algebra Boolean lattice Borel algebra Brouwerian lattice cardinal number chain condition Chapter closed sets closure commutative compact complemented lattice complemented modular lattice complete lattice completing the proof congruence relations contains Conversely Corollary countable defined definition direct product directed vector space distributive lattice dual ideal dually elements epimorphic equivalent Example Exercises exists finite length functions geometric lattice Hence identity implies integrally closed interval isomorphic isotone join l-group l-ideals lattice of finite Lemma linear Math maximal metric lattice modular lattice monoid Moreover morphism Noetherian nonvoid normal subgroup open sets ordered group ordinal ortholattice permutable po-group polynomial poset relatively complemented relatively complemented lattice result ring satisfies semimodular lattice sequence Show subalgebra subdirect product sublattice subset subspaces Theorem 12 theory topological space topology trivial upper bound valuation vector lattice whence x v y