We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propo...

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

In this paper, we introduce the concept of an M-fuzzy subgroup of an M-group and discussed some of its properties.

An M-polysymmetrical hyperring $(R,+,cdot )$ is an algebraic system, where $(R,+)$ is an M-polysymmetrical hypergroup, $(R,cdot )$ is a semigroup and $cdot$ is bilaterally distributive over $+$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this concept, we construct an ordinary quotient ring. Finally, the fundamental theorem of homomorphi...

Graph homomorphism has been studied intensively. Given an m ×m symmetric matrix A, the graph homomorphism function is defined as

Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $overline{Z}(M)$ (for short, $overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $overline{Z}(M)$, there is a nonzero homomorphism $f:dfrac{M}{N}rightarrow M$. We investigate some conditions under which the two concepts coretractable and $overline{Z}(M)$-coretractable...

A module $M$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $M$ into $M$. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.

We show that for every binary matroid $N$ there is a graph $H_*$ such the graphic $M_G$ of $G$, matroid-homomorphism from to if and only graph-homomorphism $G$ $H_*$. With this we prove complexity dichotomy problem $\rm{Hom}_\mathbb{M}(N)$ deciding $M$ admits homomorphism $N$. The polynomial time solvable has loop or no circuits odd length, otherwise $\rm{NP}$-complete. also get dichotomies lis...

Let M be a closed connected smooth manifold and G = Diff0(M) denote the connected component of the diffeomorphism group of M containing the identity. The natural action of G on M induces the trace homomorphism on homology. We show that the image of trace homomorphism is annihilated by the subalgebra of the cohomology ring of M , generated by the characteristic classes of M . Analogously, if J i...

Let M be a von Neumann algebra and ρ : M → M be a ∗-homomorphism. Then ρ is called a centrally extendable ∗-homomorphism (CEH) if there is a maximal abelian subalgebra (masa) M of the commutant M of M and a surjective ∗-homomorphism φ : M → M such that φ(Z) = ρ(Z) for all Z in the center of M. A ∗-ρderivation δ : M → M is called a centrally extendable ∗-ρ-derivation (CED) if there is a masa M o...