On the Nilpotence of the S-Radical in Matrix Near-Rings

John F.T. Hartney () and Anthony M. Matlala ()
Additional contact information
John F.T. Hartney: Univ. of Witwatersrand
Anthony M. Matlala: Univ. of Witwatersrand

A chapter in Nearrings and Nearfields, 2005, pp 217-224 from Springer

Abstract: Abstract Let R be a zero-symmetric near-ring with identity and $$M$$ n(R) the matrix near-ring associated with R. We prove that the s-radicals Js(R) and Js( $$M$$ n(R)) satisfy (Js(R))+ ⊆ Js (Mn(R)), where $$M$$ n(R) satisfies the DCCL. We also show that A+ ⊆ A, where A and A are the s-socles of R and $$M$$ n(R), respectively. The s-socle of a near-ring R is the unique minimal ideal modulo which Js(R) is non-zero and nilpotent. We further conjecture about the relationship between A and A*.

Date: 2005
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-3391-9_10

Ordering information: This item can be ordered from
http://www.springer.com/9781402033919

DOI: 10.1007/1-4020-3391-5_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().