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DTSTART;TZID=Europe/Sofia:20220128T130000
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DTSTAMP:20260628T051625
CREATED:20220124T212550Z
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SUMMARY:Семинар "Алгебра и логика"
DESCRIPTION:На 28 януари 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. \nДоклад на тема: \nBicommutative algebras from commutative point of view\nще изнесе Веселин Дренски (ИМИ – БАН). \nРезюме: The nonassociative algebra R is right-commutative if \n(ab)c = (ac)b for all a\, b\, c in R\, \nR is left-commutative if \na(bc) = b(ac) for all a\, b\, c in R. \nBicommutative algebras are algebras which are both left- and right-commutative. One-sided commutative algebras appeared for the first time in a paper by Cayley in 1857. Their important subclass of Gelfand-Dorfman-Novikov algebras were studied by Gelfand and Dorfman for the needs of the Hamiltonian operator in finite-dimensional mechanics and by Balinskii and Novikov in relation with the equations of hydrodynamics. \nDzhumadil’daev\, Ismailov and Tulenbaev described the free bicommutative algebra and in the case of characteristic 0 determined the main parameters needed in the study of varieties of bicommutative algebras. They proved that the square F2 of the free bicommutative algebra F is a commutative associative algebra. This idea was further explored by the speaker and Zhakhayev who applied classical methods of commutative algebra in the study of bicommutative algebras. \nRecently Yuxiu Bai\, Yuqun Chen and Zerui Zhang have established that the ideals of finitely generated free bicommutative algebras have finite Gröbner-Shirshov bases. In this way they have demonstrated the power of the methods of Shirshov for the study of ideals of nonassociative algebras. Bai\, Chen and Zhang also have shown the integrality of the Gelfand-Kirillov dimension of finitely generated bicommutative algebras. \nOnce results are established it is natural to search for new proofs and further generalizations. The idea of the talk is to show that many results for bicommutative algebras can be obtained with well known results in commutative algebra. Additionally this approach allows the usage of popular computer packages for calculations with bicommutative algebras. \n  \nСеминарът ще се проведе посредством платформата Zoom и всеки желаещ може да се присъедини като последва линка: \nhttps://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 \nTopic: Онлайн семинар на секция “Алгебра и логика”\nTime: Jan 28\, 2022 01:00 PM Sofia\nMeeting ID: 851 3737 5021\nPasscode: 035647 \nОт секция „Алгебра и логика” на ИМИ – БАН\nhttp://www.math.bas.bg/algebra/seminarAiL/\n============================== =====================
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%b8-%d0%bb%d0%be%d0%b3%d0%b8%d0%ba%d0%b0-draft-2/
LOCATION:Zoom
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%A1%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%20%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%20%D0%B8%20%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0":MAILTO:algebra_logic_seminar@math.bas.bg
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