The lowest eigenenergies of few, strongly interacting electrons in a one–dimensional ring are studied in presence of an impurity barrier. The persistent current I , periodic in an Aharonov–Bohm flux penetrating the ring, is strongly influenced by the electron spin. The impurity does not remove discontinuities in I at zero temperature. The total electron spin of the ground state oscillates with ...

Context. Very long baseline interferometry (VLBI) is a radio-astronomical technique whereby the correlated signal from various baselines combined into an image of highest possible angular resolution. Due to sparsity measurements, this imaging procedure constitutes ill-posed inverse problem. For decades, CLEAN algorithm has been standard choice in VLBI studies, despite it bringing on some seriou...

We show that all monomial ideals in the polynomial ring in at most 3 variables are pretty clean and that an arbitrary monomial ideal I is pretty clean if and only if its polarization I p is clean. This yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree, and it also implies that a multicomplex is shellable if and only the simplicial complex correspond...

A square matrix is said to be alternating-clean if it is the sum of an alternating matrix and an invertible matrix. In this paper, we determine all alternating-clean matrices over any division ring K. If K is not commutative, all matrices are alternating-clean, with the exception of the 1× 1 zero matrix. If K is commutative, all matrices are alternating-clean, with the exception of odd-size alt...

Let $f:A\rightarrow B$ be a ring homomorphism and $K$ an ideal of $B$. Many variations the notions clean nil-clean rings have been studied by variety authors. We investigate strongly $\pi$-regular clean-like properties amalgamation $A\bowtie^{f}K$ $A$ with $B$ along respect to $f$.

In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {it weakly $J$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $J(R)$ and the ring $R$ is called {it weakly $J$-quasipolar} if every element of $R$ is weakly $J$-quasipolar. We give many characterizations and investiga...

It is shown that a commutative Bézout ring R with compact minimal prime spectrum is an elementary divisor ring if and only if so is R/L for each minimal prime ideal L. This result is obtained by using the quotient space pSpec R of the prime spectrum of the ring R modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if R is arith...