Structural theorems for multiplicative systems of functions

1985 ◽  
Vol 46 (1-2) ◽  
pp. 111-127
Author(s):  
J. Jakubowski
Keyword(s):  
Multiplicative Systems ◽  
Structural Theorems

On multiplicative systems defined by generators and relations

1953 ◽  
Vol 49 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Trevor Evans
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Cyclic Group ◽  
Complete Information ◽  
Isomorphism Problem ◽  
Infinite Cyclic Group ◽  
Generators And Relations ◽  
Decision Method ◽  
Multiplicative Systems ◽  
Finitely Related

The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly complete information about the automorphisms and endo-morphisms of free and finitely related loops. The automorphism group of the free monogenie loop is the infinite cyclic group, each automorphism being obtained by mapping the generator on one of its repeated inverses. A monogenie loop with a finite, non-empty set of relations has only a finite number of endomorphisms. These are obtained by mapping the generator on some of the components, or their repeated inverses, occurring in the relations. We use the same methods to solve the isomorphism problem for monogenie loops, i.e. we give a method for determining whether two finitely related monogenie loops are isomorphic. The decision method consists essentially of constructing all homomorphisms between two given finitely related monogenie loops.

REMARK ON MULTIPLICATIVE SYSTEMS OF FUNCTIONS

1986 ◽  
Vol 19 (2) ◽  
Author(s):  
Jacek Jakubowski
Keyword(s):  
Multiplicative Systems

Series in multiplicative systems in Lorentz spaces

2017 ◽  
Vol 102 (3-4) ◽  
pp. 310-324
Author(s):  
S. S. Volosivets
Keyword(s):  
Lorentz Spaces ◽  
Multiplicative Systems

scholarly journals Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents

2019 ◽  
Vol 10 (1) ◽  
pp. 24-45
Author(s):  
Samuel Allen Alexander
Keyword(s):  
Structural Properties ◽  
Intelligent Agents ◽  
Intelligent Agent ◽  
Related Question ◽  
Practical Intelligence ◽  
Guiding Principle ◽  
Intelligence Measures ◽  
Open Question ◽  
Structural Theorems

Abstract Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg-Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures.

Sign in / Sign up

Export Citation Format

Share Document