Abstract. The holomorph of a discrete group G is the universal semi-direct product of G. We construct a resolution for Hol(Zpr ) for every prime p, where Zm denotes a cyclic group of order m, and use it to compute the integer homology and mod p cohomology of Hol(Zpr ) (this computation is long and is omitted here, but will appear in [V]). Also, we study maps of holomorphs of groups and maps of ...

For A ⊆ Zm and n ∈ Zm, let σ1(A, n), σ2(A, n), σ3(A, n) denote the number of solutions of the equation n = a+a′ with ordered pairs (a, a′) ∈ A, unordered pairs (a, a′) ∈ A(a = a′) and unordered pairs (a, a′) ∈ A, respectively. In this paper, for any i ∈ {1, 2, 3}, we determine all subsets A of Zm such that σi(A, n) = σi(Zm\A, n) holds for all n ∈ Zm.

A TTF-triple (C, T , F) in an abelian category is one-sided split in case either (C, T) or (T , F) is a split torsion theory. In this paper we classify one-sided split TTF-triples in module categories, thus completing Jans' classification of two-sided split TTF-triples and answering a question that has remained open for almost forty years.

In this paper, we define the notions of inverse strong non-split r-dominating set and inverse strong non-split r-domination number γ′snsr(G) of a graph G. We characterize graphs for which γsnsr(G) + γ′snsr(G) = n, where γsnsr(G) is the strong non-split r-domination number of G. We get many bounds on γ′snsr(G). Nordhaus-Gaddum type results are also obtained for this new parameter.

Let Γ(Zm) be the zero divisor graph of the ring Zm. In this paper we explore the p-partite structures of Γ(Zm), as well as determine a complete classification of the chromatic number of Γ(Zm). In particular, we explore how these concepts are related to the prime factorization of m.

Split reporter proteins capable of self-association and reactivation have applications in biomedical research, but designing these proteins, especially the selection of appropriate split points, has been somewhat arbitrary. We describe a new methodology to facilitate generating split proteins using split GFP as a self-association module. We first inserted the entire GFP module at one of several...

‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

The commuting graph of a group G, denoted by Γ(G), is the simple undirected graph whose vertices are the non-central elements of G and two distinct vertices are adjacent if and only if they commute. Let Zm be the commutative ring of equivalence classes of integers modulo m. In this paper we investigate the connectivity and diameters of the commuting graphs of GL(n,Zm) to contribute to the conje...

To evaluate the protective effect of Zataria multiflora boiss. (Zm) extract against arsenic-induced oxidative damage in rats. Rats were orally treated with various doses of Zm (200, 400, and 600 mg/kg) and sodium arsenite (5.5 mg/ kg), alone or in combination, once daily for 30 consecutive days. Twenty-four hours after the last dose, rats were euthanized, and biochemical studies were conducted ...