Loading...
Projects / Programmes source: ARIS

Mappings of rings and algebras II

Research activity

Code Science Field Subfield
1.01.01  Natural sciences and mathematics  Mathematics  Analysis 

Code Science Field
P120  Natural sciences and mathematics  Number theory, field theory, algebraic geometry, algebra, group theory 
P140  Natural sciences and mathematics  Series, Fourier analysis, functional analysis 
Keywords
functional identity, ring, algebra, homomorphism, derivation, Banach algebra, operator
Evaluation (rules)
source: COBISS
Researchers (6)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  08721  PhD Matej Brešar  Mathematics  Head  2000  830 
2.  06084  PhD Bojan Hvala  Mathematics  Researcher  1999 - 2000  243 
3.  02297  PhD Peter Legiša  Mathematics  Researcher  1998 - 2000  455 
4.  01470  PhD Bojan Magajna  Mathematics  Researcher  2000  231 
5.  00204  PhD Anton Suhadolc  Mathematics  Researcher  1997 - 2000  586 
6.  04310  PhD Joso Vukman  Mathematics  Researcher  2000  327 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,135 
Abstract
The main goal of this research is to develop the theory of functional identities in rings and to find its applications to different topics. A functional identity is, roughly speaking, an identity, holding for all elements in a ring (or some appropriate subset of a ring), which involves arbitrary mappings. When considering a functional identity, the goal is to find either the form of all maps involved or to get some information on the structure of the ring. Similarly we consider the so-called generalized functional identities where, besides arbitrary mappings, some fixed elements of the ring also appear. The concept of a functional identity can be viewed as a generalization of the concept of a polynomial identity, while the concept of a generalized functional identity extends the concept of a generalized polynomial identity. In view of the applications, however, we see that (generalized) functional identities can be considered more as a complement to the theory of (generalized) polynomial identities. Namely, definite results on functional identities can be obtained especially in those rings that do not satisfy polynomial identities. There are various problems where functional identities have been proved more efficient than other methods known so far. In particular, this holds for long-standing Herstein''s conjectures on Lie isomorphisms. One of the main purposes of the present research is to give the final settlement of these conjectures. Algebraic methods and results, obtained in our research, are also applicable to some other mathematical areas, in particular, to functional analysis and operator theory.
Views history
Favourite