Projects / Programmes source: ARRS

Preslikave na kolobarjih in algebrah (Slovene)

Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

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 
Evaluation (rules)
source: COBISS
Researchers (6)
no. Code Name and surname Research area Role Period No. of publications
1.  08721  PhD Matej Brešar  Mathematics  Principal Researcher  2001 - 2003  805 
2.  20272  PhD Maja Fošner  Administrative and organisational sciences  Researcher  2001 - 2003  214 
3.  06084  PhD Bojan Hvala  Mathematics  Researcher  2001 - 2003  243 
4.  02297  PhD Peter Legiša  Mathematics  Researcher  2001 - 2003  450 
5.  01470  PhD Bojan Magajna  Mathematics  Researcher  2001 - 2003  230 
6.  04310  PhD Joso Vukman  Mathematics  Researcher  2001 - 2003  323 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,469 
Our work is devoted to the study of various problems concerning mappings of rings and algebras. Our approach is for the most part algebraic, although a considerable number of results belong to functional analysis and operator theory. Namely, it has turned out that algebraic methods that we have developed are often useful in analysis. Our basic research topic is the theory of functional identities. The concept of a functional identity is rather new; we initiated the study of these identities in the beginning of 90's by a series of papers. Recently, an interest for this topic has increased and many fundamental contributions have been made by other mathematicians (especially K. I. Beidar and M. A. Chebotar). In a loose manner one can describe a functional identity as an identical relation satisfied by all elements in a ring (or at least from some special subset of a ring) which also involves some mappings. It should be pointed out that these mappings are entirely arbitrary, that is, we do not impose any conditions on how, for example, mappings act on the product of elements (as, for example, in Kharchenko's theory of differential identities). In the case when besides mappings some fixed elements appear in the identity, we speak about a generalized functional identity. The concept of a functional identity can be be considered as a generalization of the concept of a polynomial identity, and similarly, a generalized functional identity is a generalization of a generalized polynomial identity. A typical result on (generalized) functional identities states that a ring satisfying a certain (generalized) functional identity must either satisfy a (generalized) polynomial identity (of certain degree) or the form of the mappings involved can be precisely described. The theory of functional identities has turned out to be applicable to various problems; in particular, their results are used in solving long-standing Herstein's conjectures on Lie homomorphisms. Our goal is one the one hand to unify and extend the existing results on functional identities, and on the other hand to find their further applications in algebra (e.g. Lie and Jordan maps) as well as in analysis (e.g. preservers). We shall also consider some special types of mappings (automorphisms, derivations, elementary operators etc.) which are also studied in both algebra and analysis. In particular, we intend to find generalizations of the density theorem to rings and algebras with derivations and automorphisms.
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