On when the multiplicative center of a near-ring is a subnear-ring.
Due to the lack of one side of the distributive law, the (multiplicative) center of a nearring may not be a subnearring in general. In this article, the authors investigate when the center of a nearring is itself a subnearring. They first show that a finite simple zero-symmetric nearring \(N\) with nonzero center \(C(N)\) and \(N^2\not=\{0\}\) must have an identity. In this case, if \(C(N)\) is additively closed, then it is a field. In particular, if \(N\) is a von Neumann regular nearring with \(C(N)\) a subnearring, then \(C(N)\) is a commutative von Neumann regular ring, and hence a subdirect product of fields. They continue to describe the multiplicative center of matrix nearrings, and characterize the nearrings with identity of order \(p^2\), \(p\) a prime, that have additively closed center.
scientific article; zbMATH DE number 2113895