TY - BOOK A1 - Zhuchok, Anatolii V. T1 - Relatively free doppelsemigroups N2 - A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic K-theory. We consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. Doppelsemigroups are a generalization of semigroups and they have relationships with such algebraic structures as interassociative semigroups, restrictive bisemigroups, dimonoids, and trioids. In the lecture notes numerous examples of doppelsemigroups and of strong doppelsemigroups are given. The independence of axioms of a strong doppelsemigroup is established. A free product in the variety of doppelsemigroups is presented. We also construct a free (strong) doppelsemigroup, a free commutative (strong) doppelsemigroup, a free n-nilpotent (strong) doppelsemigroup, a free n-dinilpotent (strong) doppelsemigroup, and a free left n-dinilpotent doppelsemigroup. Moreover, the least commutative congruence, the least n-nilpotent congruence, the least n-dinilpotent congruence on a free (strong) doppelsemigroup and the least left n-dinilpotent congruence on a free doppelsemigroup are characterized. The book addresses graduate students, post-graduate students, researchers in algebra and interested readers. N2 - Eine Doppelalgebra ist eine auf einem Vektorraum definierte Algebra mit zwei binären linearen assoziativen Operationen. Doppelalgebren spielen eine herausragende Rolle in der algebraischen K-Theorie. Wir betrachten Doppelhalbgruppen, d.h Mengen mit zwei binären assoziativen Operationen, welche die Axiome der Doppelhalbgruppe erfüllen. Doppelhalbgruppen sind Veralgemeinerungen von Halbgruppen und sie stehen in Beziehung zu solchen algebraischen Strukturen wie interassoziative Halbgruppen, restriktive Bihalbgruppen, Dimonoiden und Trioden. In dieser Lecture Notes werden eine Vielzahl von Beispielen für Doppelhalbgruppen und strong Doppelhalbgruppen gegeben. Die Unabhängigkeit der Axiome für Doppelhalbgruppen wird nachgewiesen. Ein freies Produkt in der Varietät der Doppelhalbgruppen wird vorgestellt. Wir konstruieren auch eine freie (kommutative) strong Doppelhalbgruppe, eine freie n-dinilpotent (strong) Doppelhalbgruppe und eine freie Links n-dinilpotent Doppelhalbgruppe. Darüber hinaus werden die kleinste n-nilpotente Kogruenz, die kleinste n-dinilpotente Kongruenz auf der freien (strong) Doppelhalbgruppe und die kleinste n-dinilpotente Kongruenz auf einer freien Doppelhalbgruppe charakterisiert. Das Buch richtet sich an Graduierte, Doktoranden, Forscher in Algebra und interessierte Leser. T3 - Lectures in pure and applied mathematics - 5 KW - doppelsemigroup KW - interassociativity KW - free algebra KW - semigroup KW - congruence Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-407719 SN - 978-3-86956-427-2 SN - 2199-4951 SN - 2199-496X IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK ED - Denecke, Klaus-Dieter T1 - General algebra and applications T3 - Research and exposition in mathematics Y1 - 1993 SN - 3-88538-220-2 VL - 20 PB - Heldermann CY - Berlin ER - TY - BOOK ED - Denecke, Klaus-Dieter T1 - General algebra and applications in discrete mathematics : proceedings of "Conference on General Algebra and Discrete Mathematics" T3 - Berichte aus der Mathematik Y1 - 1997 SN - 3-8265-2431-4 PB - Shaker CY - Aachen ER - TY - BOOK ED - Denecke, Klaus-Dieter ED - Vogel, Hans-Jürgen T1 - General algebra and applications : proceedings of the 59th Workshop on General Algebra ; 15th Conference for Young Algebraists, Potsdam 2000 T3 - Berichte aus der Mathematik Y1 - 2000 SN - 3-8265-7983-6 PB - Shaker CY - Aachen ER - TY - BOOK ED - Gil, Juan ED - Grieser, Daniel ED - Lesch, Matthias T1 - Approaches to singular analysis : a volume of advances in partial differential equations T3 - Operator theory : advances and applications Y1 - 2001 SN - 3-7643-6518-8 U6 - https://doi.org/10.1007/978-3-0348-8253-8 VL - 125 PB - Birkhäuser Basel CY - Basel ER - TY - BOOK ED - Gil, Juan ED - Krainer, Thomas ED - Witt, Ingo T1 - Aspects of Boundary Problems in Analysis and Geometry : advances in partial differential equations T3 - Operator Theory : Advances and Applications Y1 - 2004 SN - 3-7643-7069-6 VL - 151 PB - Birkhäuser CY - Basel ER - TY - BOOK ED - Blath, Jochen ED - Imkeller, Peter ED - Roelly, Sylvie T1 - Surveys in stochastic processes Y1 - 2011 SN - 978-3-03719-072-2 PB - European Mathematical Society CY - Zürich ER - TY - BOOK ED - Schmidt, Hans-Jürgen T1 - General Relativity and Gravitation N2 - General Relativity and Gravitation is a journal of studies in general relativity and related topics, published under the auspices of the International Committee on General Relativity and Gravitation. The journal publishes original, high-quality research papers on the theoretical and experimental aspects of general relativity and related topics; surveys and review articles on current research in general relativity and gravitation; news regarding conferences and other enterprises of interest to scientists in this field; and book reviews. All manuscripts and editorial correspondence, as well as books for review, should be submitted to the Editor, and authors may propose who among the Associate Editors will deal with their paper. All submitted articles are acknowledged and refereed. Y1 - 1995 UR - http://www.kluweronline.com/issn/0001-7701/contents SN - 0001-7701 PB - Kluwer CY - Dordrecht ER - TY - BOOK ED - Läuter, Henning T1 - Statistics : a journal of theoretical and applied statistics Y1 - 1994 SN - 0233-1888 PB - Gordon & Breach Science Publ. CY - Reading Berkshire [u.a.] ER - TY - BOOK ED - Demuth, Michael ED - Schrohe, Elmar ED - Schulze, Bert-Wolfgang ED - Sjöstrand, J. T1 - Evolution equations, Feshbach resonances, singular Hodge theory T3 - Mathematical topics Y1 - 1999 SN - 3-527-40233-0 VL - 16 PB - Wiley-VCH CY - Berlin ER -