caa a22 4500 60552257X CHVBK 20210128100745.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10958-015-2381-x doi (NATIONALLICENCE)springer-10.1007/s10958-015-2381-x Applications of Local Algebras of Differentiable Manifolds [Elektronische Daten] [M. Jukl, L. Juklová, J. Mikeš] This paper is devoted to some applications of local algebras in geometry. We recall some properties of free finite-dimensional modules over local algebras of a certain type, so-called A-spaces in the sense of Macdonald, where A denotes the algebra considered. Using these properties, we study bilinear, special symmetric, and symplectic forms on A-spaces and obtain some their invariants. Properties of these spaces are used in the study of projective Klingenberg spaces over the ring A. We present fundamental notions of points and subspaces of projective Klingenberg spaces. We examine the neighborship property of points and homologies. We obtain a criterion of projective equivalence of quadrics on these spaces. Springer Science+Business Media New York, 2015 Jukl M. Dept. of Algebra and Geometry, Faculty of Science, Palacky University, Olomouc, Czech Republic aut Juklová L. Dept. of Algebra and Geometry, Faculty of Science, Palacky University, Olomouc, Czech Republic aut Mikeš J. Dept. of Algebra and Geometry, Faculty of Science, Palacky University, Olomouc, Czech Republic aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 207/3(2015-06-01), 485-511 1072-3374 207:3<485 2015 207 10958 https://doi.org/10.1007/s10958-015-2381-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2381-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jukl M. Dept. of Algebra and Geometry, Faculty of Science, Palacky University, Olomouc, Czech Republic aut NATIONALLICENCE 700 1- Juklová L. Dept. of Algebra and Geometry, Faculty of Science, Palacky University, Olomouc, Czech Republic aut NATIONALLICENCE 700 1- Mikeš J. Dept. of Algebra and Geometry, Faculty of Science, Palacky University, Olomouc, Czech Republic aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 207/3(2015-06-01), 485-511 1072-3374 207:3<485 2015 207 10958