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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
EN
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..
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Integrations on rings

64%
Banič I.
Open Mathematics
|
2017
|
tom 15
|
nr 1
365-373
EN
In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to f. The main goal of the paper is to generalize this notion of the indefinite integral from the ring of real functions to any ring. We also investigate basic properties of such generalized integrals and compare them to the well-known properties of indefinite integrals of real functions.
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