The classes of FP -injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (weakly quasi-Frobenius...

An expression in terms of (cyclotomic) harmonic sums can be simplified by the quasi-shuffle algebra in terms of the so-called basis sums. By construction, these sums are algebraically independent within the quasi-shuffle algebra. In this article we show that the basis sums can be represented within a tower of difference ring extensions where the constants remain unchanged. This property enables...

In this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. We have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. We have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

The interplay between aromaticity and hydrogen bonding in 1,3-dihydroxyaryl-2-aldehydes is investigated by means of quantum-chemical calculations. The position of the extra ring formed by substituents interacting through the hydrogen bond (HB) is found to influence both the strength of the HB and the local aromaticity of the polycyclic aromatic hydrocarbon (PAH) skeleton. The HBs are stronger a...

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

Let D be a weighted oriented graph, whose underlying graph is G , and let I (D) its edge ideal. If has no 3-, 5-, or 7-cycles, K?nig, we characterize when unmixed. 3- 5-cycles, Cohen–Macaulay. We prove that unmixed if only Cohen–Macaulay girth greater than 7 K?nig 4-cycles.

In this work, a new approach to background subtraction based on independent component analysis is presented. This approach assumes that background and foreground information are mixed in a given sequence of images. Then, foreground and background components are identified, if their probability density functions are separable from a mixed space. Afterwards, the components estimation process cons...

This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3 investigates the correlation with well-known Prüfer conditions; namely, we prove that this class of rings stands strictly between the two classes of arithmetical...