Abstract
V.V. Shchigolev has proven that over any infinite field k of characteristic p > 2 , the T-space generated by G = { x 1 p , x 1 p x 2 p , … } is finitely based, which answered a question raised by A.V. Grishin. Shchigolev went on to conjecture that every infinite subset of G generates a finitely based T-space. In this paper, we prove that Shchigolev's conjecture was correct by showing that for any field of characteristic p > 2 , the T-space generated by any subset { x 1 p x 2 p ⋯ x i 1 p , x 1 p x 2 p ⋯ x i 2 p , … } , i 1 < i 2 < i 3 < ⋯ , of G has a T-space generating set of size at most i 2 − i 1 + 1 .
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 callSimilar Papers
Disclaimer: 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.
