Дифференциальная алгебра

Amsterdam - Oxford - New York.: North-Holland Publishing Company. 1979. - 374p. - ISBN: 0-444-85292-1, English. ( OCR-Слой ). (North-Holland Mathematical Library. Volume 21 ). This book is mainly devoted to the study of some rings of differential operators. The three basic examples are An(C), Dn and Ep. An(C) is the Weyl algebra whose elements are differential operators with...

Paris.: Hermann, 1994. — 179 p. (Actualites mathematiques). English. ( OCR-Слой ). The object of diophantine geometry is the study of the sets of rational points of algebraic varieties. The classical case is the "arithmetic case" when our varieties are defined over a number field. One soon discoveres however that most arithmetic diophantine questions have interesting "geometric...

Berlin.: Springer, 1992. — 145 p. (Lecture Notes in Mathematics. 1506 ). — ISBN: 3-540-55181-6, English. ( OCR-Слой ). Differential algebraic groups are defined roughly speaking as "groups of solutions of algebraic differential equations" in the same way in which algebraic groups are defined as "groups of solutions of algebraic equations". They were introduced in modern...

Berlin.: Springer, 1986. — 147 p. (Lecture Notes in Mathematics. 1226 ). — Online ISBN: 978-3-540-47354-1, English. ( OCR-Слой ). Our background consists of two theories each having quite classical roots namely: A) The theory of algebraic differential equations (AOE's with no movable singularity and B) The Galois theory of ADE'e. The first theory was initiated by Fuchs,...

New York: John Wiley & Sons, 1965. — 355 c. Difference Rings and Difference Fields Relations Among Difference Rings Ritt Difference Rings Varieties of Difference Polynomials Extensions of Difference Fields Systems of Difference Equations Isomorphisms of Difference Fields The Variety of a Difference Polynomial

UK. Cambridge.: Cambridge University Press, 1995. — 209 p. (London Mathematical Society Student Texts. 33 ). — ISBN: 0-521-55908-1, English. ( OCR-Слой ). As its title says, this book is only a primer; in particular, you will learn very little 'grammar' from it. That is not surprising; to speak the language of algebraic D-modules fluently you must first learn some algebraic...

Paris.: Hermann, 1957. — 63 p. (ACTUALITES SСIENTIFIQUES ET INDUSTRIELLES. 1251 ). English. ( OCR-Слой ). Differential algebra is easily described: it is (99 per cent or more) the work of Ritt and Kolchin. I have written this little book to make the subject more easily accessible to the mathematical community. Ritt was at heart an analyst; but the subject is algebra. As a...

N.Y.: AP, 1973. — 448 p. (Pure and Applied Mathematics. 54 ). English. ( OCR-Слой ). [A series of Monographs and Textbooks. Editors: Paul A. Smith and Samuel Eilenberg]. It is common knowledge that algebra, including algebraic geometry, historically grew out of the study of algebraic equations with numerical coefficients. In much the same way, differential algebra sprang from...

UK. London.: AP, 1985. — 273 p. ((Pure and Applied Mathematics. 114 ). — ISBN: 0-12-417640-2, English. ( OCR-Слой ). During the past 35 years the theory of algebraic groups has grown from infancy to vigorous maturity and has been widely applied to other fields of mathematics. Because algebraic equations form a special case of algebraic differential equations, it is natural to...

UK.: Gordon and Breach, Science Publishers, Inc., 1983. — (759+viii) p., (Mathematics and Its Applications. 15 ). — 1SBN 0-677-05670-2, ISSN: 0543-0941, English. ( OCR-Слой ). On 31st May 1832, Evariste Galois died at the age of 21_ At that time the word "group" was not even used in mathematics, and the work of Galois that introduced it for the first time did not become known...

Providence, Rhode Island: American Mathematical Society, 1950. — 184+viii p. — (Colloquium Publications. Vol. 33). In 1932, the author published Differential equations from the algebraic standpoint, a book dealing with differential polynomials and algebraic differential manifolds. In the sixteen years which have passed, the work of a number of mathematicians has given fresh...

М.: Издательство иностранной литературы, 1959. — 85 с. Брошюра И. Капланского знакомит читателя с основами современной дифференциальной алгебры и с возможными путями развития этой науки. В ней излагаются, в частности, основы теории Галуа для дифференциальных полей, т. е. теории Пикара — Вессио в ее современном виде. Брошюра эта будет очень полезна для математиков самых...

В этой монографии крупного французского ученого трактуется ряд важных вопросов современного анализа (теоремы о продолжении, неравенство Лоясевича, подготовительная теорема Вейерштрасса — Мальгранжа, проблема деления Лорана Шварца и т. д. ). Изложение сжатое, но доступное для начинающих. Математики всех специальностей найдут в книге много для себя интересного. Она будет полезна...