Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource (xv, 387 p.) , ill , 25 cm

Edition: Online-Ausgabe Elsevier e-book collection on ScienceDirect Sonstige Standardnummer des Gesamttitels: 041169-3

ISBN: 0444824383 , 9780444824387

Series Statement: North-Holland mathematics studies 184

Note: Includes bibliographical references (p. 369-376) and index

Additional Edition: Reproduktion von Alternative loop rings 1996

Language: English

Subjects: Mathematics

URL: Volltext

URL: Volltext  (Deutschlandweit zugänglich)

URL: Inhaltstext

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Format: XV, 387 S. : graph. Darst.

ISBN: 0-444-82438-3

Series Statement: North-Holland mathematics studies 184

Language: English

Subjects: Mathematics

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007677273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: Inhaltsverzeichnis

URL: http://www.loc.gov/catdir/enhancements/fy0601/96038501-d.html

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007677273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

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Format: 1 online resource (404 p.)

ISBN: 1-281-22272-0 , 9786611222727 , 0-08-052706-X

Series Statement: North-Holland mathematics studies ; 184

Content: For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously. One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups. Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and grou

Note: Description based upon print version of record. , Cover; Contents; Preface; Introduction; Chapter I. Alternative Rings; 1. Fundamentals; 2. The real quaternions and the Cayley numbers; 3. Generalized quaternion and Cayley-Dickson algebras; 4. Composition algebras; 5. Tensor products; Chapter II. An Introduction to Loop Theory and to Moufang Loops; 1. What is a loop?; 2. Inverse property loops; 3. Moufang loops; 4. Hamiltonian loops; 5. Examples of Moufang loops; Chapter III. Nonassociative Loop Rings; 1. Loop rings; 2. Alternative loop rings; 3. The LC property; 4. The nucleus and centre; 5 . The norm and trace; Chapter IV. RA Loops , 1. Basic properties of RA loops2. RA loops have LC; 3. A description of an RA loop; Chapter V. The Classification of Finite RA Loops; 1. Reduction to indecomposables; 2. Finite indecomposable groups; 3. Finite indecomposable RA loops; 4. Finite RA loops of small order; Chapter VI. The Jacobson and Prime Radicals; 1. Augmentation ideals; 2. Radicals of abelian group rings; 3. Radicals of loop rings; 4. The structure of a semisimple alternative algebra; Chapter VII. Loop Algebras of Finite Indecomposable RA Loops; 1. Primitive idempotents of commutative rational group algebras , 2. Rational loop algebras of finite RA loopsChapter VIII. Units in Integral Loop Rings; 1. Trivial torsion units; 2. Bicyclic and Bass cyclic units; 3. Trivial units; 4. Trivial central units; 5. Free subgroups; Chapter IX. Isomorphisms of Integral Alternative Loop Rings; 1. The isomorphism theorem; 2. Inner automorphisms of alternative algebras; 3. Automorphisms of alternative loop algebras; 4. Some conjectures of H. J. Zassenhaus; Chapter X. Isomorphisms of Commutative Group Algebras; 1. Some results on tensor products of fields; 2. Semisimple abelian group algebras , 3. Modular group algebras of abelian groups4. The equivalence problem; Chapter XI. Isomorphisms of Loop Algebras of Finite RA Loops; 1. Semisimple loop algebras; 2. Rational loop algebras; 3. The equivalence problem; Chapter XII. Loops of Units; 1. Reduction to torsion loops; 2. Group identities; 3. The centre of the unit loop; 4. Describing large subgroups; 5. Examples; Chapter XIII. Idempotents and Finite Conjugacy; 1. Central idempotents; 2. Nilpotent elements; 3. Finite conjugacy; Bibliography; Index; Notation , English

Additional Edition: ISBN 0-444-82438-3

Language: English

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Format: xi, 371 Seiten : , Illustrationen.

ISBN: 1-4020-0238-6 , 1-4020-0239-4

Series Statement: Algebras and applications 1

Note: Includes bibliographical references (p. 351-363) and index

Language: English

Subjects: Mathematics

Keywords: Gruppenring

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009879416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

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Format: XI, 371 S , graph. Darst. , 25 cm

ISBN: 1402002386

Series Statement: Algebras and applications 1

Note: Literaturverz. S 351 - 363

Language: English

Subjects: Mathematics

Keywords: Gruppenring ; Gruppenring

URL: Inhaltstext

URL: http://www.loc.gov/catdir/enhancements/fy0822/2001050674-d.html

URL: http://www.loc.gov/catdir/enhancements/fy0822/2001050674-t.html

UID:

Format: xi, 371 Seiten , Illustrationen

ISBN: 1402002386 , 1402002394

Series Statement: Algebras and applications 1

Note: Includes bibliographical references (p. 351-363) and index

Language: English

Subjects: Mathematics

Keywords: Gruppenring

URL: Inhaltsverzeichnis

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Format: 1 online resource (vii, 270 p.)

Edition: Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

ISBN: 9780821881781 (online)

Series Statement: Contemporary mathematics, v. 499

Note: The radical of the four generated algebra of alternating type / , Globalization of partial actions on semiprime rings / , The Colombeau quaternion algebra / , Parabolic subgroups of real direct limit Lie groups / , Parabolic sets of roots / , Some results on $\ast $-minimal algebras with involution / , Invariants of partial group algebras of finite $p$-groups / , Units of $\Bbb ZC_p$ / , Algebraic elements as free factors in simple Artinian rings / , Special units, unipotent units and free groups in group algebras / , Explicit realizations of simple weight modules of classical Lie superalgebras / , Combinatorial aspects in the computation of proper multiplicities / , An estimate of the dimension of the varieties of alternative and Jordan algebras / , On growth of almost polynilpotent Lie algebras / , Graded identities for Lie algebras / , Polynomial codimension growth of graded algebras / , Euclidean Bianchi groups are conjugacy separable / , Comparability, distributivity and non-commutative $\phi $-rings / , Algebras having bases consisting entirely of units / , On the growth of varieties of algebras / , 0-dialgebras with bar-unity, Rota-Baxter and 3-Leibniz algebras / , The Golod-Shafarevich counterexample without Hilbert series / , Automorphism groups of semi-homogeneous trees / , Mode of access : World Wide Web

Additional Edition: Print version: Groups, rings, and group rings : ISSN 0271-4132 ISBN 9780821847718

Language: English

Keywords: Electronic books.

URL: Contents

URL: Contents

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Format: 1 online resource (viii, 324 p. : ill.)

Edition: Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

ISBN: 9780821882160 (online)

Series Statement: Contemporary mathematics, v. 537

Note: Linear codes over $\Bbb F_q[u]/(u^t)$ / , Globalization theorems for partial Hopf (co)actions, and some of their applications / , On Nichols algebras associated to simple racks / , Pointed Hopf algebras with standard braiding are generated in degree one / , Asymptotics of Young tableaux in the $(k,\ell )$ hook / , Classification of irreducible representations over finite simple Lie conformal superalgebras / , Pure gaps and bounds for the generalized Hamming weights of Goppa codes / , Exact divisibility of exponential sums over the binary field via the covering method / , All hereditary torsion theories are higher differential / , A categorical approach to classical and quantum Schur-Weyl duality / , Partial actions: a survey / , On free associative algebras linearly graded by finite groups / , Gelfand-Tsetlin categories / , On growth of codimensions of Jordan algebras / , Geometric Weil representations for star-analogues of $SL(2,k)$ / , Exceptional sequences, braid groups and clusters / , Spherical distributions of some generalized Gelfand pairs attached to the Heisenberg group / , On the linearity and quasi-cyclicity of the gray image of codes over a Galois ring / , Some applications of Frobenius algebras to Hopf algebras / , The algebra of differential operators associated to a weight matrix: a first example / , Mode of access : World Wide Web

Additional Edition: Print version: Groups, algebras and applications : ISSN 0271-4132 ISBN 9780821852392

Language: English

Keywords: Electronic books.

URL: Contents

URL: Contents

URL: Click to View