In this paper, we study the relation between m-strongly Gorenstein projective (resp. injective) modules and n-strongly Gorenstein projective (resp. injective) modules whenever m 6= n, and the homological behavior of n-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Goren...

Let g be a finite dimensional, complex, reductive Lie algebra. One says that a symmetric, g-invariant, R(resp. C)-bilinear form on g is a Manin form if and only if its signature is (dimCg, dimCg) (resp. is non degenerate). Recall that a Manin-triple in g is a triple (B, i, i), where B is a real (resp. complex) Manin form and where i, i are real (resp. complex) Lie subalgebras of g, isotropic fo...

Let f : X → Y be a perfect surjective map of metrizable spaces. It is shown that if Y is a C-space (resp., dimY ≤ n and dim f ≤ m), then the function space C(X, I ∞ ) (resp., C(X, I 2n+1+m )) equipped with the source limitation topology contains a dense Gδ-set H such that f ×g embeds X into Y × I ∞ (resp., into Y × I 2n+1+m ) for every g ∈ H. Some applications of this result are also given.

Suppose that f (resp. g) is a modular form of integral (resp. half-integral) weight with coefficients in the ring of integers OK of a number field K. For any ideal m ⊂ OK , we bound the first prime p for which f | Tp (resp. g | Tp2) is zero (mod m). Applications include the solution to a question of Ono [AO] concerning partitions.

As general concepts of sup-hesitant fuzzy right (resp., left, interior, two-sided) ideals semigroups, the sup+α-hesitant and sup-β-hesitant are introduced their properties investigated. Then, established by sets, Łukasiewicz anti-fuzzy Pythagorean hesitant hybrid interval-valued sets cubic sets. Finally, we characterize which is intra-regular, completely regular, simple semigroups or another ty...

In the present paper, we continue the study on fuzzy soft topological spaces and investigate the properties of fuzzy soft semi connected sets, fuzzy soft semi separated sets and fuzzy soft semi s-connected sets and have established several interesting properties supported by examples. Moreover, we show that a fuzzy soft semi disconnectedness property is not hereditary property in general. Final...

A hybrid structure is a mapping defined by integrating soft set and fuzzy set. Therefore, the concept of structures an abstraction sets sets. As result, we can apply (resp., fuzzy) ideals in ordered semigroups to settings. In present paper, introduce notion n-interior id="M2"> id="m...

following the idea of $l$-fuzzy neighborhood system as introduced byfu-gui shi, and its generalization to $(l,m)$-fuzzy neighborhood system, the relationship between  $(l,m)$-fuzzy topology and $(l,m)$-fuzzy neighborhood system will be further studied. as an application of the obtained results, we will describe the initial structures of $(l,m)$-fuzzy neighborhood subspaces and $(l,m)$-fuzzy top...