LEADER 03798nam  22007095  450 
001 9910254308803321
005 20220329224328.0
010   $a3-319-53907-8
024 7 $a10.1007/978-3-319-53907-2
035   $a(CKB)3710000001127301
035   $a(DE-He213)978-3-319-53907-2
035   $a(MiAaPQ)EBC4833895
035   $a(PPN)199767556
035   $a(EXLCZ)993710000001127301
100   $a20170330d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aFormal matrices /$fby Piotr Krylov, Askar Tuganbaev
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (VIII, 156 p.)
225 1 $aAlgebra and Applications,$x1572-5553 ;$v23
311   $a3-319-53906-X 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Construction of Formal Matrix Rings of Order 2 -- Modules over Formal Matrix Rings -- Formal Matrix Rings over a Given Ring -- Grothendieck and Whitehead Groups of Formal Matrix Rings.
330   $aThis monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.
410  0$aAlgebra and Applications,$x1572-5553 ;$v23
606   $aAssociative rings
606   $aRings (Algebra)
606   $aCategory theory (Mathematics)
606   $aHomological algebra
606   $aK-theory
606   $aMatrix theory
606   $aAlgebra
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086
606   $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094
615  0$aAssociative rings.
615  0$aRings (Algebra).
615  0$aCategory theory (Mathematics).
615  0$aHomological algebra.
615  0$aK-theory.
615  0$aMatrix theory.
615  0$aAlgebra.
615 14$aAssociative Rings and Algebras.
615 24$aCategory Theory, Homological Algebra.
615 24$aK-Theory.
615 24$aLinear and Multilinear Algebras, Matrix Theory.
676   $a512.9434
700   $aKrylov$b Piotr$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767413
702   $aTuganbaev$b Askar$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254308803321
996   $aFormal Matrices$92141282
997   $aUNINA