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Rings Graded By a Generalized Group

100%

Fatehi F., Molaei M. R.

Topological Algebra and its Applications

2014

tom 2

nr 1

The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups. We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian module..

K-quasiderivations

100%

Emmons C., Krebs M., Shaheen A.

Open Mathematics

2012

tom 10

nr 2

824-834

A K-quasiderivation is a map which satisfies both the Product Rule and the Chain Rule. In this paper, we discuss several interesting families of K-quasiderivations. We first classify all K-quasiderivations on the ring of polynomials in one variable over an arbitrary commutative ring R with unity, thereby extending a previous result. In particular, we show that any such K-quasiderivation must be linear over R. We then discuss two previously undiscovered collections of (mostly) nonlinear K-quasiderivations on the set of functions defined on some subset of a field. Over the reals, our constructions yield a one-parameter family of K-quasiderivations which includes the ordinary derivative as a special case.

Ograniczanie wyników

1 Open Mathematics

1 Topological Algebra and its Applications

1 Emmons C.

1 Fatehi F.

1 Krebs M.

1 Molaei M. R.

1 Shaheen A.

1 2014

1 2012

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Rings Graded By a Generalized Group

K-quasiderivations