### SYARAT PERLU DAN CUKUP ELEMEN NORMAL PADA RING DENGAN ELEMEN SATUAN

*Titi Udjiani SRRM  -  Dept. of Mathematics, Universitas Diponegoro, Indonesia

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Abstract

In a ring with involution, it is possible to collect elements that are commutative with elements obtained from the results of the involution operation on itself. Such elements are called normal elements. On other hand,  rings with  involution  have elements that have Moore Penrose inverse. Elements that have  Moore Penrose inverse are not always normal. This paper discusses the necessary and sufficient conditions for elements that have  Moore Penrose inverse  is normal. The method used is  determine  set of elements that have  Moore Penrose inverse. Then take  normal elements  and determine sufficient conditions. Investigate whether the sufficient condition is a necessary condition. If yes, we obtain the necessary and sufficient condition. If not, determine else sufficient conditions for can be added to obtain the necessary and sufficient conditions.

Keywords: Ring, Normal, Moore, Penrose.
Funding: Universitas Diponegoro under contract MetMu123456

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : ID
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