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Paediatric Intestinal Enteroids Derived from Very Early Onset Inflammatory Bowel Disease Reveal Differences in Growth, Morphology, and Barrier Function

Balakrishnan V, Selvam B, B SR, Dutta AK, Joseph AJ, Simon E, Ramani S, Estes M, Ward H, Pulimood A, Ajjam SS.   +10 more
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Graded Semiartinian Rings: Graded Perfect Rings

Communications in Algebra, 2003
Abstract We study graded left semiartinian rings with finite support. It is shown that the semiartinian property is preserved when we pass to the smash product in the sense of Quinn. We apply these results to investigate left perfect graded rings.
C. Năstăsescu, L. Dăuş, B. Torrecillas   +2 more
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Graded π-rings

Canadian Journal of Mathematics, 1979
All rings considered will be commutative with identity. By a graded ring we will mean a ring graded by the non-negative integers.A ring R is called a π-ring if every principal ideal of R is a product of prime ideals. A π-ring without divisors of zero is called a π-domain.
Anderson, D. D., Matijevic, J.
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Artinian Semigroup-Graded Rings

Bulletin of the London Mathematical Society, 1995
Let \(S\) be a semigroup with no infinite subgroups and let \(R\) be a right Artinian \(S\)-graded ring. We prove that \(R\) necessarily has finite support.
Clase, M. V., Jespers, E., Kelarev, A. V., Okniński, J.   +3 more
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Graded Quotient Rings

Journal of Mathematical Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Graded radicals of graded rings

Acta Mathematica Hungarica, 1991
Let \(\lambda\) be a radical property in the category of associative rings and \(G\) a group. By means of the smash product a corresponding radical property \(\lambda_{\text{ref}}\) is defined in the category of associative \(G\)-graded rings. The authors describe these radicals and the relationship with the corresponding classical graded radicals for ...
Beattie, M., Stewart, P.
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Graded varieties of graded rings

Acta Mathematica Hungarica, 1995
\(G\)-graded rings with an identity are considered where \(G\) is a finite group. First the concept of a graded variety is introduced and the graded version of Birkhoff's Theorem is proved. A proper subclass \({\mathcal V}\) of all \(G\)-graded rings is a graded radical graded semisimple class if and only if \({\mathcal V} \subseteq {\mathcal D}^g ...
Sands, A. D., Yahya, H.
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Weakly primitive graded rings

Russian Mathematical Surveys, 2001
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Quotient rings of graded associative rings. I

Journal of Mathematical Sciences, 2012
The paper under review is a survey concerning graded quotient rings of associative rings graded by groups. Some new results are also included. The paper is structured in ten sections as follows: 1. Basic definitions and properties, 2. Graded analogs of classical notions, 3. Graded rational extensions and rings of quotients, 4.
Balaba, I. N., Kanunnikov, A. L., Mikhalev, A. V.   +2 more
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