On rings whose Morita class is represented by matrix rings

Differential Polynomial Rings of Triangular Matrix Rings

On Rings Whose Associated Lie Rings Are Nilpotent

We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...

Strongly Clean Matrix Rings over Commutative Rings

A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local ring...

On Skew Triangular Matrix Rings

For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring Tn(R,α). By using an ideal theory of a skew triangular matrix ring Tn(R,α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x;α]/〈xn〉, for each positive integer n, where R[x;α] is the skew polynomial ring, and 〈xn〉 is the ideal generated by xn.

A class of J-quasipolar rings

In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {it weakly $J$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $J(R)$ and the ring $R$ is called {it weakly $J$-quasipolar} if every element of $R$ is weakly $J$-quasipolar. We give many characterizations and investiga...