in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

The author proves that, if S is an FIC-semigroup or a completely regular semigroup, and if RS is a ring with identity, then R < E(S) > is a ring with identity. Throughout this paper, R denotes as a ring with identity. Let S be a semigroup, X ⊆ S . The following notations are used in the paper: < X > : the subsemigroup of S generated by X ; |X| : the cardinal number of X ; E(S): the set of idemp...

The crystal structure of the title compound, C(17)H(16)N(2)O(3)S, exhibits intra-molecular C-H⋯S and inter-molecular C-H⋯S and C-H⋯O hydrogen bonds, C-S⋯N [S⋯N = 3.033 (2) Å and C-S⋯N = 142.76 (9)°] inter-actions, and C-H⋯π inter-actions; these inter-actions generate S(4), S(6) and R(2) (2)(14) ring motifs. The isoxazole ring adopts an envelope conformation, with the N atom displaced by 0.672 (...

Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...

In the title pyrazoline derivative, C(14)H(12)ClN(3)S(2), the thiophene ring is disordered over two orientations with a refined site-occupancy ratio of 0.832 (4):0.168 (4). The pyrazoline ring adopts an envelope conformation with the C atom linking the thiophene ring at the flap. The dihedral angles between the benzene ring and the major and minor components of the thiophene ring are 88.6 (3) a...

Goldie’s Theorem (1960), which is one of the most important results in Ring Theory, is a criterion for a ring to have a semisimple left quotient ring. The aim of the paper is to give four new criteria (using a completely different approach and new ideas). The first one is based on the recent fact that for an arbitrary ring R the set M of maximal left denominator sets of R is a non-empty set [2]...

MR0044509 (13,427c) 09.0X Artin, Emil; Tate, John T. A note on finite ring extensions. J. Math. Soc. Japan 3 (1951), 74–77. Let R and S be two commutative rings, R ⊆ S. Then S is called a modulefinite extension of R, if it is an R-module with a finite set of generators, that is, if there exists a finite number of elements of S such that every element of S can be represented as a linear combinat...

We give a description of the kernel of the induction map K0(R) → K0(S), where S is a commutative ring and R = S G is the ring of invariants of the action of a finite group G on S. The description is in terms of H(G,GL(S)).