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Semicommutativity of the rings relative to prime radical

Handan Kose, Burcu Ungor (2015)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we introduce a new kind of rings that behave like semicommutative rings, but satisfy yet more known results. This kind of rings is called P -semicommutative. We prove that a ring R is P -semicommutative if and only if R [ x ] is P -semicommutative if and only if R [ x , x - 1 ] is P -semicommutative. Also, if R [ [ x ] ] is P -semicommutative, then R is P -semicommutative. The converse holds provided that P ( R ) is nilpotent and R is power serieswise Armendariz. For each positive integer n , R is P -semicommutative if and...

Semifields and a theorem of Abhyankar

Vítězslav Kala (2017)

Commentationes Mathematicae Universitatis Carolinae

Abhyankar proved that every field of finite transcendence degree over ℚ or over a finite field is a homomorphic image of a subring of the ring of polynomials ℤ [ T 1 , ⋯ , T n ] (for some n depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.

Semiprime rings with nilpotent Lie ring of inner derivations

Kamil Kular (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

We give an elementary and self-contained proof of the theorem which says that for a semiprime ring commutativity, Lie-nilpotency, and nilpotency of the Lie ring of inner derivations are equivalent conditions

Semirings embedded in a completely regular semiring

M. K. Sen, S. K. Maity (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Recently, we have shown that a semiring S is completely regular if and only if S is a union of skew-rings. In this paper we show that a semiring S satisfying a 2 = n a can be embedded in a completely regular semiring if and only if S is additive separative.

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