… introduce an extension of the classical trivial extension of rings to extensions associated to
… In Theorem 3.9, we show that the ntrivial extension of a finite direct product of rings is a finite …

… We also study trivial ring extensions which are fqp-rings. The class of fqp-rings was introduced
… We get a complete characterization of trivial ring extensions which are fqp-ring only in the …

… In this paper, using the construction technique of trivial extensic~is, we give counter-examples
to four questions on rings and modules raised, respectively, by PF Smith [2], PF Smith and …

… a trivial ring extension R M and compare some ring theoretic properties of R and R M such
as left SF rings, left V -rings, left Kasch rings, left PS rings. … RM is a left Kasch ring if and only if …

The author wishes to express her gratitude to Professors MauriceAuslander, Robert Fossum
and Phillip Griffith, for invaluable inspirationand assistance. In particular, much of this work …

… trivial extension ring inherit the properties of the ring and present the relationship between
the trivial … Thus we proved that if is an Artinian ring, then the trivial extension is a -regular ring. …

… The @-trivial extension of R by M is the ring whose underlying set is the Cartesian product …
trivial extension R K M. The main purpose of this paper is to investigate the @-trivial extension …

… ring extensions of commutative rings by modules. Namely, we prove that the trivial ring extension
R: = A ⋉ B defined by extension … divisor ring if and only if A is an elementary divisor ring …

… This section develops a result on the transfer of the (n, d)-property for a particular context of
trivial ring extensions, namely, those issued from local (not necessarily Noetherian) rings by …

… It is well known that commutative artinian QF-1 rings are QF, but Osofsky has … , ring which
is a trivial extension of a valuation ring. It is shown that if a trivial extension of a valuation ring is …