Based on a completely distributive lattice M , we propose new fuzzification approach to module, which leads the concept of an id="M2"> -hazy module. Different from traditional that defines fuzzy algebra as subset classical algebra, introduce id="M3"> module by fuzzifications algebraic operations. Then, investigate fundam...

We compare the K-theory and K-homology of the well known CAR algebra. While the K0 group is infinitely generated, we show that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology group is very large. These results give some insight into the K-homology of AF-algebras. 1. The CAR algebra We...

We provide more characterizations of varieties having a term Mal’cev modulo two functions F and G. We characterize varieties neutral in the sense of F , that is varieties satisfying R ⊆ F (R). We present examples of global operators satisfying the homomorphism property, in particular we show that many known commutators satisfy the homomorphism property. See Parts I-III [2] for unexplained notat...

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte’s generalization of the Chern–Weil homomorphism.

We define the Lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing, demonstrating its applicability.

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

We find the universal module w(M) for functions (that need not be invariants) of finite matroids, defined on a minor-closed class M and with values in any module L over any commutative and unitary ring, that satisfy a parametrized deletion-contraction identity, F (M) = δeF (M r e) + γeF (M/e), when e is neither a loop nor a coloop. (F is called a (parametrized) weak Tutte function.) Within the ...

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from affine super Yangian [Formula: see text] to universal enveloping algebra of rectangular W-superalgebra for all m ≠ n, m, n ≥ 2 or 3, = 0. Furthermore, show that image this is dense, provided k + ( − n)( l 1)