Serial factorizations of right ideals
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DOI: 10.1016/j.jpaa.2018.02.030
Abstract: In a Dedekind domain $D$, every non-zero proper ideal $A$ factors as a product $A=P_1^{t_1}\cdots P_k^{t_k}$ of powers of distinct prime ideals $P_i$. For a Dedekind domain $D$, the $D$-modules $D/P_i^{t_i}$ are uniserial. We extend… read more here.
Keywords: serial factorizations; factorizations right; right ideals;
Associated primes and primary right ideals of generalized triangular matrix rings
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DOI: 10.1080/00927872.2018.1508579
Abstract: Abstract Let be an (S, R)-bimodule of the rings R and S. We determine the associated primes of a formal triangular matrix ring Indeed, we show that We then obtain necessary and sufficient conditions for… read more here.
Keywords: triangular matrix; matrix; right ideals; associated primes ... See more keywords
Right ideal decompositions of nearrings with faithful 2-step modules
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DOI: 10.1080/00927872.2024.2398632
Abstract: Abstract When N is a left nearring with identity satisfying the descending chain condition on right ideals N can be written as a direct sum of nonzero right ideals that cannot be further decomposed into… read more here.
Keywords: ideal decompositions; step; decompositions nearrings; faithful step ... See more keywords
On rings all of whose right ideals are automorphism-invariant
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DOI: 10.1080/00927872.2024.2447493
Abstract: Abstract Rings all of whose right ideals are automorphism-invariant are called right a-rings. It is shown that (1) local right a-rings are left duo, (2) local rings whose left ideals of R are invariant under… read more here.
Keywords: ideals automorphism; whose right; rings whose; right ring ... See more keywords