A right R-module M is called a Goldie module if it has finite Goldie dimension and satisfies
the ACC for M-annihilator submodules of M. In this paper, we study the class of prime Goldie …

For an R-module M, projective in σ [M] and satisfying ascending chain condition on left
annihilators, the authors introduce the concept of Goldie module. The authors also use the …

Using the concepts of prime module, semiprime module and the concept of ascending chain
condition (ACC) on annihilators for an R-module M, we prove that if M is semiprime and …

Let M be a semiprime Goldie module which is projective in σ [M]. We give several
decompositions of the M-injective hull M ̂ of M in terms of its minimal prime submodules …

PRIME SUBMODULES OF ARTINIAN MODULES Page 1 TAIWANESE JOURNAL OF
MATHEMATICS Vol. 13, No. 6B, pp. 2011-2020, December 2009 This paper is available online at …

We prove that if R is an idempotent reflexive left Goldie ring whose simple singular left R-
modules are GP-injective, then R is a finite product of simple left Goldie rings. As a …

In this paper modules with ascending chain condition (acc)(respectively, with descending
chain conditon (dcc)) on essential submodules are investigated: Finitely generated quasi …

Let R be a semiprime, right Goldie ring, with semisimple Artinian right quo-tient ring Q (R). If
M is a right R-module, then the Goldie rank of M, written Grkº M, or Grk M if the context is …

In this article, we study the second radical of a module over an arbitrary ring R as the dual
notion of the prime radical of a module. We give some properties of the second radical and …

Let R be a ring and M a right R‐module. It is shown that (1) δ (M) is Noetherian if and only if
M satisfies ACC on δ‐small submodules;(2) δ (M) is Artinian if and only if M satisfies DCC on …