{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:19:26Z","timestamp":1742912366113,"version":"3.40.3"},"publisher-location":"Cham","reference-count":18,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319328584"},{"type":"electronic","value":"9783319328591"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-32859-1_31","type":"book-chapter","created":{"date-parts":[[2016,4,15]],"date-time":"2016-04-15T11:12:06Z","timestamp":1460718726000},"page":"362-376","source":"Crossref","is-referenced-by-count":3,"title":["Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions"],"prefix":"10.1007","author":[{"given":"Alexander","family":"Levin","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,4,16]]},"reference":[{"key":"31_CR1","unstructured":"Einstein, A.: The Meaning of Relativity. Appendix II (Generalization of gravitation theory), 4th edn., pp. 133\u2013165. Princeton (1953)"},{"key":"31_CR2","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1090\/S0002-9904-1964-11203-9","volume":"70","author":"ER Kolchin","year":"1964","unstructured":"Kolchin, E.R.: The notion of dimension in the theory of algebraic differential equations. Bull. Am. Math. Soc. 70, 570\u2013573 (1964)","journal-title":"Bull. Am. Math. Soc."},{"issue":"2","key":"31_CR3","doi-asserted-by":"publisher","first-page":"92","DOI":"10.2307\/1970810","volume":"89","author":"JL Johnson","year":"1969","unstructured":"Johnson, J.L.: K\u00e4hler differentials and differential algebra. Ann. Math. 89(2), 92\u201398 (1969)","journal-title":"Ann. Math."},{"key":"31_CR4","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/BF02564523","volume":"44","author":"JL Johnson","year":"1969","unstructured":"Johnson, J.L.: A notion on Krull dimension for differential rings. Comment. Math. Helv. 44, 207\u2013216 (1969)","journal-title":"Comment. Math. Helv."},{"key":"31_CR5","first-page":"201","volume":"192","author":"JL Johnson","year":"1974","unstructured":"Johnson, J.L.: K\u00e4hler differentials and differential algebra in arbitrary characteristic. Trans. Am. Math. Soc. 192, 201\u2013208 (1974)","journal-title":"Trans. Am. Math. Soc."},{"key":"31_CR6","unstructured":"Kolchin, E.R.: Some problems in differential algebra. In: Proceedings of the International Congress of Mathematicians (Moscow - 1966), Moscow, pp. 269\u2013276 (1968)"},{"key":"31_CR7","volume-title":"Differential Algebra and Algebraic Groups","author":"ER Kolchin","year":"1973","unstructured":"Kolchin, E.R.: Differential Algebra and Algebraic Groups. Academic Press, New York (1973)"},{"key":"31_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1257-6","volume-title":"Differential and Difference Dimension Polynomials","author":"MV Kondrateva","year":"1999","unstructured":"Kondrateva, M.V., Levin, A.B., Mikhalev, A.V., Pankratev, E.V.: Differential and Difference Dimension Polynomials. Kluwer Academic Publishers, Dordrecht (1999)"},{"issue":"1","key":"31_CR9","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1070\/RM1980v035n01ABEH001588","volume":"35","author":"AB Levin","year":"1980","unstructured":"Levin, A.B.: Characteristic polynomials of inversive difference modules and some properties of inversive difference dimension. Russ. Math. Surv. 35(1), 217\u2013218 (1980)","journal-title":"Russ. Math. Surv."},{"key":"31_CR10","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1006\/jsco.1999.0412","volume":"30","author":"AB Levin","year":"2000","unstructured":"Levin, A.B.: Reduced Groebner bases, free difference-differential modules and difference-differential dimension polynomials. J. Symb. Comput. 30, 357\u2013382 (2000)","journal-title":"J. Symb. Comput."},{"issue":"5","key":"31_CR11","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/j.jsc.2006.05.006","volume":"42","author":"AB Levin","year":"2007","unstructured":"Levin, A.B.: Gr\u00f6bner bases with respect to several orderings and multivariable dimension polynomials. J. Symb. Comput. 42(5), 561\u2013578 (2007)","journal-title":"J. Symb. Comput."},{"key":"31_CR12","doi-asserted-by":"crossref","unstructured":"Levin, A.B.: Computation of the strength of systems of difference equations via generalized Gr\u00f6bner bases. In: Grobner Bases in Symbolic Analysis, pp. 43\u201373. Walter de Gruyter (2007)","DOI":"10.1515\/9783110922752.43"},{"key":"31_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-6947-5","volume-title":"Difference Algebra","author":"AB Levin","year":"2008","unstructured":"Levin, A.B.: Difference Algebra. Springer, New York (2008)"},{"issue":"2\u20133","key":"31_CR14","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s11786-010-0048-z","volume":"4","author":"AB Levin","year":"2010","unstructured":"Levin, A.B.: Dimension polynomials of intermediate fields and Krull-type dimension of finitely generated differential field extensions. Math. Comput. Sci. 4(2\u20133), 143\u2013150 (2010)","journal-title":"Math. Comput. Sci."},{"key":"31_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/978-3-642-54479-8_7","volume-title":"Algebraic and algorithmic aspects of differential and integral operators","author":"AB Levin","year":"2014","unstructured":"Levin, A.B.: Multivariate dimension polynomials of inversive difference field extensions. In: Barkatou, M., Cluzeau, T., Regensburger, G., Rosenkranz, M. (eds.) AADIOS 2012. LNCS, vol. 8372, pp. 146\u2013163. Springer, Heidelberg (2014)"},{"key":"31_CR16","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1090\/conm\/184\/02123","volume":"184","author":"AB Levin","year":"1995","unstructured":"Levin, A.B., Mikhalev, A.V.: Type and dimension of finitely generated G-algebras. Contemp. Math. 184, 275\u2013280 (1995)","journal-title":"Contemp. Math."},{"key":"31_CR17","volume-title":"Computer Algebra. Calculations in Differential and Difference Algebra","author":"AV Mikhalev","year":"1989","unstructured":"Mikhalev, A.V., Pankratev, E.V.: Computer Algebra. Calculations in Differential and Difference Algebra. Moscow State Univ. Press, Moscow (1989)"},{"key":"31_CR18","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1090\/S0002-9947-1975-0406992-9","volume":"212","author":"W Sit","year":"1975","unstructured":"Sit, W.: Well-ordering of certain numerical polynomials. Trans. Am. Math. Soc. 212, 37\u201345 (1975)","journal-title":"Trans. Am. Math. Soc."}],"container-title":["Lecture Notes in Computer Science","Mathematical Aspects of Computer and Information Sciences"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-32859-1_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,1,20]],"date-time":"2019-01-20T23:45:25Z","timestamp":1548027925000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-32859-1_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319328584","9783319328591"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-32859-1_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}