000 03189nam a22004455i 4500
001 978-0-8176-4642-4
003 DE-He213
005 20140220083227.0
007 cr nn 008mamaa
008 111215s2012 xxu| s |||| 0|eng d
020 _a9780817646424
_9978-0-8176-4642-4
024 7 _a10.1007/978-0-8176-4642-4
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
100 1 _aKnoebel, Arthur.
_eauthor.
245 1 0 _aSheaves of Algebras over Boolean Spaces
_h[electronic resource] /
_cby Arthur Knoebel.
264 1 _aBoston, MA :
_bBirkhäuser Boston :
_bImprint: Birkhäuser,
_c2012.
300 _aXII, 331p. 63 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Introduction -- Algebra -- Tools -- Complexes and their Sheaves -- Boolean Subsemilattices -- Sheaves from Factor Congruences -- Shells -- Baer-Stone Shells -- Strict Shells -- Varieties Generated by Preprimal Algebras -- Return to General Algebras -- Further Examples Pointing to Future Research -- List of Symbols -- References -- Index.
520 _aSheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. Sheaves decompose general algebras into simpler pieces called the stalks. A classical case is commutative von Neumann regular rings, whose stalks are fields. Other classical theorems also extend to shells, a common generalization of rings and lattices. This text presents intuitive ideas from topology such as the notion of metric space and the concept of central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why central elements in rings and lattices have their particular form. Categorical formulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stone’s theorem for Boolean algebras. Half of the theorems provided in the text are new; the rest are presented in a coherent framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas are outlined, including a final chapter summarizing applications of sheaves in diverse fields that were not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellent reference text for those who wish to learn about sheaves of algebras.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aTopology.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aTopology.
650 2 4 _aCategory Theory, Homological Algebra.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817642181
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4642-4
912 _aZDB-2-SMA
999 _c100212
_d100212