Muhamad Faikar Mustafidz Al Habibi, Santi Irawati, Hery Susanto, I. Made Sulandra, Hidetoshi Marubayashi, Angelina Yan Mui Chin
A subring R of a simple artinian ring Q is said to be a Dubrovin valuation ring if R is a Bezout order and R/J(R) is simple artinian, where J(R) is the Jacobson radical of R. It is known that Q is a simple artinian ring if and only if Q is isomorphic to Mn(D), for some division ring D and n ∈. On the other hand, a ring R is said to be nil-clean if each element a ∈ R can be expressed as a = e + n for some idempotent element e ∈ R and nilpotent element n ∈ R. There does not appear to be any studies on connections between these two concepts. In this article, we find sufficient conditions for a Dubrovin valuation ring of a simple artinian ring to be a nil-clean ring. © 2019 Author(s).
Department of Mathematics, Universitas Negeri Malang, Jalan Semarang 5, Malang, 65145, Indonesia; Department of Mathematics, Naruto University of Education, Tokushima, Japan; Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, 50603, Malaysia
