Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory matrix near-rings. A near-ring differs from a ring that it does not need to be abelian and one distributive laws hold general. We introduce two ways which near-rings can defined discuss structure each. One is as given by Beildeman other Meldrum. his normal arrays under operation multiplication additi...

Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...

We collected soil samples at 23 sites from the petroleum contaminated soils (PC) in the west of Kermanshah province to investigate the sources and ecological risk of polycyclic aromatic hydrocarbons (PAHs). In this study, source apportionment has been carried out using Positive Matrix Factorization (PMF).The total PAHs concentration, have a mean value of 92.79 mg/kg, ranging from 7.37 to 609.67...

We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers. 2000 Mathematics Subject Classification. 11C20, 11D79, 11T23

In this paper, we introduce a new concept of generalized matrix rings and build up the general theory of radicals for g.m.rings. Meantime, we obtain r̄b(A) = g.m.rb(A) = ∑ {rb(Aij) | i, j ∈ I} = rb(A)

We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.

In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.

In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.

Following a method by Meldrum and van der Walt, near-rings of matrix maps are defined for general near-rings, not necessarily with identity. The influence of one-sided identities is discussed. When the base near-ring is integral and planar, the near-ring of matrix maps is shown to be simple. Various types of primitivity of the near-ring of matrix maps are discussed when the base near-ring is pl...

1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...