Nearrings of functions without identity determined by a single subgroup
Publish place: The Journal of Algebra and Related Topics، Vol: 9، Issue: 1
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JART-9-1_009
تاریخ نمایه سازی: 31 تیر 1403
Abstract:
Let (G, +) be a finite group, written additively with identity ۰, but not necessarily abelian, and let H be a nonzero, proper subgroup of G. Then the set M = \{f : G \to G\ |\ f(G) \subseteq H \ \hbox{and}\ f(۰) = ۰ \} is a right, zero-symmetric nearring under pointwise addition and function composition. We find necessary and sufficient conditions for M to be a ring and determine all ideals of M, the center of M, and the distributive elements of M.
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