In this paper, using the equivalence between category of crossed modules algebras and algebra-algebroids, we will explore notions ideality factors for these algebraic structures. We give structure a two sided ideal an algebra-algebroid notion quotient algebra-algebroid. By considering algebra-algebroid, show that module corresponding to is Conversely, by taking module, also module.

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra to geometr...

In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.

We consider the intuitionistic fuzzification of the concept of prime ideals in commutative BCK-algebras, and investigate some of their properties. We show that if P is a prime ideal of commutative BCK-algebra X iff ∼ P = 〈XP , − XP 〉 is an intuitionistic fuzzy prime ideal of X. We also prove that An IFS A = 〈μA, λA〉 of commutative BCK-algebra X is an intuitionistic fuzzy prime ideal of X if and...

In this paper, we acquaint new kinds of ideals BCK-algebras built on tripolar picture fuzzy structures. fact, the notions ideal, implicative ideal (commutative ideal) BCK-algebra are introduced, and related properties studied. Also, a relation among is well-known. Furthermore, it shown that may be but converse not correct in common. Further, obtained an BCK-algebra, aforementioned statement tru...

In this paper, we will show a reduction of ideal arithmetic, or more generally, of arithmetic of ZZ{modules of full rank in orders of number elds to problems of linear algebra over ZZ=mZZ, where m is a possibly composite integer. The problems of linear algebra over ZZ=mZZ will be solved directly, instead of either \reducing" them to problems of linear algebra over ZZ or factoring m and working ...

Let A be a Banach algebra. Then A the second dual of A is a Banach algebra with first (second) Arens product. We study the Arens products of A(= (A∗∗)∗∗). We fined some conditions on A to be a left ideal in A. We fined the biggest two sided ideal I of A, in which I is a left (right) ideal of A∗∗.

The Joseph ideal is a special ideal in the universal enveloping algebra of a simple Lie algebra. For the classical groups, its uniqueness is equivalent to the existence of tensors with special properties. The existence of these tensors is usually concluded abstractly but here we present explicit formulae. This allows a rather direct computation of a parameter used in defining the Joseph ideal.

then the ideal (F1, ..., FN) they generate in the Paley-Wiener algebra Ê ′(Rn) is slowly decreasing respect to the Paley-Wiener weight p(z) = log |z| + |Im z|. As a consequence, this ideal is closed in Ê ′(Rn). It coincides with the ideal [I(F1, ..., FN)]loc, which consists of elements in Ê ′(Rn) that belong locally to the ideal generated by F1, ..., FN in the algebra of entire functions in n v...