Lattice Concepts of Module Theory (Kluwer Texts in the Mathematical Sciences)

Rating:
Summary: A good new graduate text in abstract algebra
Review: The student who wishes to understand module theory needs to have an understanding of the several results from lattice theory . This well-written text seeks to bring together all of the results that can be brought to bear on this subject into one self contained text that includes, not only the necessary basics of lattice theory, but detailed proofs of all the results in a manner that makes the subject approachable. Beginning with a basic definition of a lattice and its well known properties, the text moves on to materials on lattice theory from recent texts on module theory. Several new concepts by the author such as fully invariant extending lattices are interspersed throughout the text. In addition to a useful index and a comprehensive list of references, more than fifty pages are devoted to solutions to a comprehensive list of exercises(forty in the first chapter and about a dozen in each of the others). This text seems to fill a gap. It is readable and well done.

Rating:
Summary: A good new graduate text in abstract algebra
Review: The student who wishes to understand module theory needs to have an understanding of the several results from lattice theory . This well-written text seeks to bring together all of the results that can be brought to bear on this subject into one self contained text that includes, not only the necessary basics of lattice theory, but detailed proofs of all the results in a manner that makes the subject approachable. Beginning with a basic definition of a lattice and its well known properties, the text moves on to materials on lattice theory from recent texts on module theory. Several new concepts by the author such as fully invariant extending lattices are interspersed throughout the text. In addition to a useful index and a comprehensive list of references, more than fifty pages are devoted to solutions to a comprehensive list of exercises(forty in the first chapter and about a dozen in each of the others). This text seems to fill a gap. It is readable and well done.