We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2. This implies that the projective dimension of any countably generated FP-injective module over an Archimedean chain ring is less or equal to 3. By [7, Theorem 1], for any module G over a commutative arithmetical ring R the weak dimension of G ...

The transfer of multiple protons in hydrogen-bonded networks usually occurs one proton at a time. At sufficiently high temperatures, each proton transfers via thermally activated hopping along its hydrogen bond, thereby moving a charge defect through the network. At low temperatures, quantum-mechanical tunnelling might set in instead, thus avoiding hopping over the energy barriers. In the case ...

The notion of FTF ring (see Definition 1.1 or Proposition 1.2) captures homological and finiteness properties shared by several classes of rings. Thus coherent rings with left flat-dominant dimension ≥ 1 [3, Corolario 2.2.11] or rings having quasi-Frobenius two-sided maximal quotient ring [7, Proposition 3.6; 3, Teorema 2.3.10] are examples of FTF rings. Moreover, FTF ring and QF-3 ring are rel...

The extensive use of computers in mathematics and engineering has led to an increased demand for reliability in the implementation of algorithms in computer algebra systems. One way to increase the reliability is to formally verify that the implementations satisfy the mathematical theorems stating their specification. By implementing and specifying algorithms from computer algebra inside a proo...

We study an entangled two-mode coherent state within the framework of2×2-dimensional Hilbert space. We investigate the problem of quantum teleportation ofa superposition coherent state via an entangled coherent channel. By three differentmeasures with the titles ``minimum assured fidelity (MASF)”, ``average teleportationfidelity” and ``optimal fidelity (f)” we study the ...

Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also play the role actual degrees freedom, and hence allow for viable implementation cold-atom based devices qubit systems. In this work, we exhaustively investigate ground state properties low-lying energy spectrum two linearly...

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

Crocus sativus L. (saffron) is a widely used food additive for its color and taste. The hypotensive effects of saffron have been shown in previous studies. The aim of this study was to evaluate the mechanism of vasodilatory effects induced by saffron on isolated rat aorta.To study the vasodilatory effects of saffron aqueous extract (0.5, 1 and 2 mg/mL), isolated rat thoracic aorta rings were co...