Motivated by a result of Traverso and Swan on seminormality, we prove that for a ring extension A subset of B, A is subintegrally closed in B if and only if the group of invertible A-submodules of B is canonically isomorphic to the group of invertible A[X]-submodules of B[X]. We also examine a relationship between these two groups in the general case, i.e. when A may not be subintegrally closed in B. (C) 2013 Elsevier Inc. All rights reserved
A module M is called an extending (or CS) module provided that every submodule of M is essential in ...
AbstractLet R be a commutative Noetherian local ring, and denote by modR the category of finitely ge...
AbstractLet R be a ring. An R-module X is called c-injective if, for every closed submodule L of eve...
Let A subset of B be an extension of commutative reduced rings and M subset of N an extension of pos...
AbstractWe prove that the A[T]-submodule I(b) introduced earlier by the authors is invertible if and...
AbstractWe show that the isomorphism ζB/A: B/A→I(A★,B★) introduced by the second author for a subint...
We show that the isomorphism ς<SUB>B/A</SUB>: B/A → ϑ(A<SUB>∗</SUB>,B<SUB>∗</SUB>) introduced by the...
Abstract. If i: A ⊂ B is a commutative ring extension, we show that the group I(A,B) of invertible A...
In a previous paper the last two authors introduced a condition which gave an elementwise characteri...
AbstractIn a previous paper the last two authors introduced a condition which gave an elementwise ch...
In a recent paper, Aydogdu and Lopez-Permouth have defined a module M. to be N-subinjective if every...
AbstractWe give an elementary and essentially self-contained proof that a reduced ring R is seminorm...
AbstractWe describe some basic facts about the weak subintegral closure of ideals in both the algebr...
If S is a subnormalizing extension [7] of a ring R with identity generated by a set which is a multi...
AbstractGiven modules M and N, M is said to be N-subinjective if for every extension K of N and ever...
A module M is called an extending (or CS) module provided that every submodule of M is essential in ...
AbstractLet R be a commutative Noetherian local ring, and denote by modR the category of finitely ge...
AbstractLet R be a ring. An R-module X is called c-injective if, for every closed submodule L of eve...
Let A subset of B be an extension of commutative reduced rings and M subset of N an extension of pos...
AbstractWe prove that the A[T]-submodule I(b) introduced earlier by the authors is invertible if and...
AbstractWe show that the isomorphism ζB/A: B/A→I(A★,B★) introduced by the second author for a subint...
We show that the isomorphism ς<SUB>B/A</SUB>: B/A → ϑ(A<SUB>∗</SUB>,B<SUB>∗</SUB>) introduced by the...
Abstract. If i: A ⊂ B is a commutative ring extension, we show that the group I(A,B) of invertible A...
In a previous paper the last two authors introduced a condition which gave an elementwise characteri...
AbstractIn a previous paper the last two authors introduced a condition which gave an elementwise ch...
In a recent paper, Aydogdu and Lopez-Permouth have defined a module M. to be N-subinjective if every...
AbstractWe give an elementary and essentially self-contained proof that a reduced ring R is seminorm...
AbstractWe describe some basic facts about the weak subintegral closure of ideals in both the algebr...
If S is a subnormalizing extension [7] of a ring R with identity generated by a set which is a multi...
AbstractGiven modules M and N, M is said to be N-subinjective if for every extension K of N and ever...
A module M is called an extending (or CS) module provided that every submodule of M is essential in ...
AbstractLet R be a commutative Noetherian local ring, and denote by modR the category of finitely ge...
AbstractLet R be a ring. An R-module X is called c-injective if, for every closed submodule L of eve...
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