• INFINITE SUB-NEAR-FIELDS OF INFINITE NEAR-FIELDS AND NEAR LEFT ALMOST – NEAR- FIELDS (IS-NF-INF-NLA-NF)
Abstract
In this paper, I studied and obtain some results on every infinite associative near-field contains an infinite commutative sub-near-field, and thereby suggested the problem of finding reasonably small classes of infinite near-fields with the property that every infinite near-field contains a sub-near-field belonging to . Clearly, there is no minimal class in the obvious sense, for in any class satisfying a near-field may be replaced by any proper infinite sub-near-field of itself. We determine a class 0 satisfying and consisting of familiar and easily-described zero symmetric near-fields; and we indicate how my results subsume and extend known finiteness results formulated in terms of sub-near-fields and zero divisors.
In last section identifies classes which satisfy and are minimal in a certain loose sense, and it extends the major result of the other sections to distributive near left almost near-fields. The field-theoretic results are proved in the setting of the alternative near-fields.
In last section identifies classes which satisfy and are minimal in a certain loose sense, and it extends the major result of the other sections to distributive near left almost near-fields. The field-theoretic results are proved in the setting of the alternative near-fields.
Keywords
Fields, Near-fields, Near – Ring, Infinite sub-near-fields, dnlan-f, near-field-theoretic.
Full Text:
PDFThis work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2010-2022 International Journal of Mathematical Archive (IJMA) Copyright Agreement & Authorship Responsibility |