Communications in Algebra

Bellue, L.P.

doi: 10.1080/00927879108824234pmid: N/A

Carl, Faith

doi: 10.1080/00927879108824235pmid: N/A

If R is a ring, and A right annulet(= annihilator right ideal) then A[X] is a right annulet of the polynomial ring R[X]. (In factX can be any set of variables.). An annulet I of R[X] of this form is said to be be extended. Not all annulets of R[X] are extended, since e.g., the ascending chain on right annulets (= acc ┴) is not inherited by R[X], as, Kerr [Ke] observed. Nevertheless, maximal (minimal) annulets of a polynomial ring R[X] are extended, as a theorem of McCopy on annihilators in R[X] readily shows (see Introduction).

Andre, Leroy; Jerzy, Matczuk

doi: 10.1080/00927879108824236pmid: N/A

For the Ore extension R[t, S,D], where R is a prime ring, we describe prime having zero intersection with R.

Jerzy, Matczuk

doi: 10.1080/00927879108824237pmid: N/A

We introduce a concept of centrally closed Hopf module algebras and show that centrally closed Hopf module algebras inherit all basic properties of centrally closed algebras.

Warren, Dicks; Hartley, B.

doi: 10.1080/00927879108824238pmid: N/A

Pere, Ara; Jae Keol, Park

doi: 10.1080/00927879108824239pmid: N/A

Max—Albert, Knus; Aidan, Schofield

doi: 10.1080/00927879108824240pmid: N/A

Limanov, L. Makar

doi: 10.1080/00927879108824241pmid: N/A

In this note two subalgebras of the skew field of fractions of the first Weyl algebra are described. One is isomorphic to the group ring of a free group with two generators. Another is maximal in the class of subalgebras with finite Gelfand-Kirillov dimension.

Ferran, Cedó

doi: 10.1080/00927879108824242pmid: N/A

By giving new examples of Mal'cev domains, i.e. domains that can not be embedded in any skew field, we answer in the negative some questions of Faith on zip rings.

Michel, Hacque

doi: 10.1080/00927879108824243pmid: N/A