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Rings of congruence preserving functions.
C J Maxson1, Frederik Saxinger2
11Department of Mathematics, Texas A&M University, College Station, TX 77843-3368 USA.
Monatshefte Fur Mathematik
|October 27, 2018
Summary
This study explores when the near-ring of congruence preserving functions on a group G becomes a ring. It examines the group
Area of Science:
- Abstract algebra
- Group theory
- Near-ring theory
Background:
- Near-rings are algebraic structures generalizing rings.
- Congruence preserving functions on groups form a near-ring.
- Understanding when this near-ring is a ring is a key question in algebra.
Purpose of the Study:
- To determine the conditions under which the near-ring of congruence preserving functions of a group G is a ring.
- To explore the relationship between the group structure of G and the ring properties of its congruence preserving functions.
Main Methods:
- Investigating the lattice structure of normal subgroups of G.
- Analyzing internal structural properties of the group G.
Main Results:
- Characterization of groups G for which the near-ring of congruence preserving functions is a ring.
- Identification of specific group properties that ensure the near-ring becomes a ring.
Conclusions:
- The ring property of the near-ring of congruence preserving functions is directly linked to the lattice of normal subgroups and the internal structure of the group G.
- Provides criteria for classifying groups based on the algebraic properties of their function near-rings.
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