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An effective procedure for minimal bases of ideals in Z[x]

100%
Cáceres-Duque L.
Discussiones Mathematicae - General Algebra and Applications
|
2003
|
tom 23
|
nr 1
5-11
EN
We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.
2
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A Note on Additive Groups of Some Specific Associative Rings

100%
Woronowicz M.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
219-229
EN
Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.
3
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On ideals of a skew lattice

75%
Costa J. P.
Discussiones Mathematicae - General Algebra and Applications
|
2012
|
tom 32
|
nr 1
5-21
EN
Ideals are one of the main topics of interest when it comes to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear. Though, skew ideals, derived from the partial order, seem to be closer to the specific nature of skew lattices. In this paper we review ideals in skew lattices and discuss the intersection of this with the study of the coset structure of a skew lattice.
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