The main purpose of this paper is a wide generalization one the results abstract algebraic geometry begins with, namely fact that prime spectrum $${\mathrm {Spec}}(R)$$ unital commutative ring R always spectral (= coherent) topological space. In generalization, which includes several other known ones, role ideals played by elements an complete lattice L equipped with binary multiplication $$xy\...

We study $$(\sigma ,\tau )$$ -derivations of a group ring RG where G is with center having finite index in and R semiprime 1 such that either has no torsion elements or if p-torsion elements, then p does not divide the order let $$\sigma $$ be R-linear endomorphisms fixing pointwise. generalize Main Theorem 1.1 Chaudhuri (Comm Algebra 47(9): 3800–3807, 2019) prove there $$T\supset R$$ $$\mat...

This paper is concerned with partially defined derivations on Banach algebras and particularly on C*-algebras and H*-algebras, a subject whose study was motivated by the question of time evolution and spatial translation in quantum physics (see [2, 7] for a full account of the theory). It is well known [4] that everywhere defined derivations on semisimple Banach algebras are automatically conti...

In this paper we shall introduce the concept of prime and semiprime bi-ideals of ordered semigroups and we give characterizations of prime bi-ideal and regular of ordered semigroups. Mathematics Subject Classification: 06F05

We reduce the problem of factoring a semiprime integer to the problem of (numerically) integrating a certain highly oscillatory function. We provide two algorithms to address this problem, one based on the residue theorem and the other in the (extended) Cauchy’s argument principle. In the former algorithm, we show that computing the residue of the function at a certain pole leads to obtaining t...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

In this paper, we discuss some basic properties of rough intuitionistic fuzzy set in semigroup. Intuitionistic fuzzy analogues of some results concerning rough semiprime (semiprimary) ideals in semigroup are obtained. 2010 AMS Classification: 03E72, 03F55, 06B10.

It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...