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It is known that an ideal of a direct product of commutative unitary rings is directly decomposable into ideals of the corresponding factors. We show that this does not hold… Click to show full abstract
It is known that an ideal of a direct product of commutative unitary rings is directly decomposable into ideals of the corresponding factors. We show that this does not hold in general for commutative rings and we find necessary and sufficient conditions for direct decomposability of ideals. For varieties of commutative rings, we derive a Mal’cev type condition characterizing direct decomposability of ideals and we determine explicitly all varieties satisfying this condition.
Keywords:
ideals direct;
products rings;
direct products
Journal Title: Asian-European Journal of Mathematics
Year Published: 2018
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Journal Title: Asian-European Journal of Mathematics
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!