Abstract
Let ( A, ω) be a kth-order Bernstein algebra and let N be the kernel of ω. This article studies the structure of such algebras in which N 2 has dimension one. The algebras are of two types, I and II, according as N 2 ⊆ U or N 2 ⊈ U. A characterization of the algebras of type I is given. Power associative kth-order Bernstein algebras with dim N 2 = 1 are then considered: they turn out to be Bernstein algebras of at most second order, and multiplication tables for these algebras over the real field are given. Finally, second-order Bernstein algebras of type II are examined and a structure theorem for them is obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
