23 citations · 44 across the 34 of their papers we have counts for
7 papers · 1 filter
Fuchs' problem for endomorphisms of abelian groups
Sunil K. Chebolu, Keir Lockridge
László Fuchs posed the following question: which abelian groups arise as the group of units in a ring? In this paper, we investigate a related question: for such realizable groups…
Rings with an elementary abelian -group of units
Sunil K. Chebolu, Jeremy Corry, Elizabeth Grimm +1
What are all rings for which (the group of invertible elements of under multiplication) is an elementary abelian -group? We answer this question for finite-dimensi…
How many units can a commutative ring have?
Sunil K. Chebolu, Keir Lockridge
Laszlo Fuchs posed the following problem in 1960, which remains open: classify the abelian groups occurring as the group of all units in a commutative ring. In this note, we provid…
When is a subgroup of a ring an ideal?
Sunil K. Chebolu, Christina L. Henry
Let be a commutative ring. When is a subgroup of an ideal of ? We investigate this problem for the rings and .…
Fuchs' problem for indecomposable abelian groups
Sunil K. Chebolu, Keir Lockridge
More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the group of units of a commutative ring. Though progress has been made, the question remains open. We provid…
What is special about the divisors of 12?
Sunil K. Chebolu, Michael Mayers
Let R be the ring of polynomials in finitely many commuting variables with coefficients in Z_n. It is shown that every unit of R is an involution if and only of n is a divisor of 1…