In this paper, we give a condition under which a bounded linear operator on a
complex Banach space has Single Valued Extension Property (SVEP) but does not have decomposition
property (±). We also discuss the analytic ...
Motivated by the theory of weighted shifts on directed trees and its multivariable counterpart, we address the question of identifying commutant and reflexivity of the multiplication d-tuple on a reproducing kernel Hilbert ...
The wandering subspace problem for an analytic norm-increasing -isometry on a Hilbert space asks whether every -invariant subspace of can be generated by a wandering subspace. An affirmative solution to this problem for ...
Let T = (V, E) be a leafless, locally finite rooted directed tree.
We associate with T a one parameter family of Dirichlet spaces Hq (q
1), which turn out to be Hilbert spaces of vector-valued holomorphic
functions ...
We systematically develop the multivariable counterpart of the theory of
weighted shifts on rooted directed trees. Capitalizing on the theory of product
of directed graphs, we introduce and study the notion of multishifts ...
Let be a rooted directed tree with finite branching index
, and let
be a left-invertible weighted shift on . We show that
can be modelled as a multiplication operator
on a reproducing kernel Hilbert space of -valued ...
Let R be a commutative ring with unity and S be a (unital) subring of R such that R is integral over S and S⊆R has FCP. Let M be an R-module. For any submodule N of M, it is shown that R(+)N⊆R(+)M has FCP if and only if ...
The following result was proved in [5,Remark 2.2].
Theorem 0.1. If R T are Noetherian rings such that there does not
exist any integrally dependent adjacent Noetherian rings between them, then
for each ¯c/¯b 2 T/Z ...
Let R be a commutative ring with identity. The ring R × R can be
viewed as an extension of R via the diagonal map : R →֒ R×R, given
by (r) = (r, r) for all r ∈ R. It is shown that, for any a, b ∈ R, the
extension ...
The notion of maximal non valuative domain is introduced and characterized.
An integral domain R is called a maximal non valuative domain
if R is not a valuative domain but every proper overring of R is
a valuative ...
Let R be a commutative ring with unity. The notion of maximal non valuation
domain in an integral domain is introduced and characterized. A proper subring R of an
integral domain S is called a maximal non valuation domain ...
Let R be a commutative ring with identity. If a ring R is contained in an arbitrary union of rings, then R is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained ...
This paper is a sequel. The earlier paper introduced, for any (unital) extension of (commutative
unital) rings R T, an invariant L(T=R) defined as the supremum of the lengths of chains of intermediate
fields in the ...
In this note, we show that a part of Ratliff (Proc Am Math Soc 101(3):395–402, 1987, Remark 2.2) is not correct. Some conditions are given under which the same holds.
Let H denotes the set of all commutative rings R in which the set of all nilpotent elements, denoted by Nil(R), is a prime ideal of R and is comparable to every ideal of R. Let R∈H be a ring and T(R) be its total quotient ...
The notion of maximal non-ϕ-pseudo-valuation ring is introduced which generalizes the concept of maximal non-pseudo-valuation domain. The equivalence of maximal non-ϕ-PVR and maximal non-local ring is established under ...
Kumar, Rahul(The Korean Mathematical Society., 2023-01)
Let H0 be the set of rings R such that Nil(R)=Z(R) is a divided prime ideal of R. The concept of maximal non ϕ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in H0. This ...
Let H0 denote the set of all rings R such that Nil(R) is a divided prime ideal with Nil(R)=Z(R). We study the concept of maximal non-λ-rings in class H0 and generalize the results of maximal non-λ-domains.