**COMMUNICATIONS IN ALGEBRA**

Volume 27, Number 1, 1999

**CONTENTS**

**The Loewy Structure of the Projective Modules of the Mathieu**

**Group Mi2 and Its Automorphism Group in Characteristic 3 . . . 1**

*S. Koshitani and K. Waki*

**The Green Correspondents of the Mathieu Group M^ in**

**Characteristic 3 . . . 37**

*S. Koshitani and K. Waki*

**Double Extension of Quadratic Lie S u p e r a l g e b r a s . . . 67**

*H. Benamor and S. Benayadi*

**Co-Cohen-Macaulayness of Certain Graded Artinian M o d u l e s . . . 89**

*Z. Tang and G. Zhu*

**On Two Open Problems About Embedding of Modules in Free**

**Modules . . . 105**

*J . Rada and M. Saorin*

**Extended Root Graphs for Complex Reflection Groups . . . 119**
*M. Hughes*

**A Minimality Property of Rees V a l u a t i o n s . . . 149**

*A. Nobile*

**Vertex-Primitive Vi -Arc-Transitive Graphs of Smallest Order . . . 163****S.-F. DuandM.-Y. Xu**

**Maximal Orders in Semigroups . . . 173**

*J . Fountain, V. Gould, and P. Smith*

**Direct Topologies from Discrete Rings. II. . . . 189**
*N. Shell*

**Quasi-P Radicals of r - R i n g s . . . 219**
*W. Chen*

*(continued on inside back cover)*

M A R C E L

MARCEL DEKKER, INC. NEW YORK • BASEL

Contributions to this journal are published free of charge

D E K K E R

**COMMUNICATIONS IN ALGEBRA**

Volume 27, Number 2, 1999

*CONTENTS*

Cyclic Representations of the Quantum Matrix Algebras . . . 493
*H. P. Jakobsen and H. Zhang*

**On the Structure of Cohen-Macaulay Simplicial AfTine**

**S e m i g r o u p s . . . 511**
*J. C. Resales and P. A. Garcia-Sdnchez*

**Elementary Groups and Invertibility for Kantor Pairs . . . 519**
*B. N. Allison and J. R. Faulkner*

*Products of Involutions in the Groups of Lie Type F ^ K ) . . . 557*

*P. C. Austin*

Gerbes and Covers . . . 577
*P. Debes andJ.-C. Douai*

**Enlargements, Semiabundancy, and Unipotent M o n o i d s . . . 595**

*J . Fountain, G. M. S. Gomes, and V. Gould*

**On the Cohomological 2-Dimension of F i e l d s . . . 615**

*R. Elman and C. Lum*

**A Note on the Wielandt Subgroup of a Metabelianp-Group... 621**

*E. A. Ormerod*

Kaplansky Fields and ^-Algebraically Closed Fields . . . 629
*P. Vamos*

**Hochschild Cohomology of Truncated Quiver Algebras . . . 645**
*A. C. Locateli*

**Rings Having a Morita-Like E q u i v a l e n c e . . . 665**

*J . L. Garcia and L. Marin*

**Large Subdirect Products of Graded M o d u l e s . . . 681**

*L. Oyonarte and B. Torrecillas*

**An Explicit Sign Formula for the Determinant of Cohomology... 703**
*W. Aitken*

**vii**

**viii CONTENTS**
**The Homotopy Type of Spaces X with Fundamental Groupoid Q**

**and an Unique Non-trivial Homotopy ^-Module Fin (X) . . . 725**

*M. Bullejos and J . G. Cabello*

**Intertwining Operators Between Some Spaces of Differential**

**Operators on a Manifold . . . 755**

*P. Mathonet*

**Generalized Verma Modules over the Lie Algebra of Type G^ . . . Ill**

*A. Khomenko and V. Mazorchuk*

**On a Characterization of Perfect Rings . . . 785**

*N. Ding and J . Chen*

**Differential Identities of Lie Ideals or Large Right Ideals in**

**Prime Rings . . . 793**

*T.-K. Lee*

**Residual Division, Primary Decomposition, and Filtrations.**

**Application to Dedekind Domains . . . 811**

*K. E. Abalo and D. N. Niango*

**Algebraic Extensions of Graded and Valued F i e l d s . . . 821**

*V.-5. Hwang and A. R. Wads-worth*

**Twisted Flag Varieties of Trialitarian G r o u p s . . . 841**
*R. S. Garibaldi*

**The Automorphism Group and the Picard Group of a Monomial**

**A l g e b r a . . . 857**

*F. Guil-Asensio and M. Saorin*

**On Some Classes of /P-Modules and Congruences in /?-Tors . . . 889**

*F. Raggi, H. Rincon, and C. Signoret*

**A PBW Basis for Lusztig's Form of Untwisted Affine Quantum**

**Groups . . . 903**
*F. Gavarini*

**Almost Finite Modules . . . 919**
*D. Apassov*

**Jordan Centroids . . . 933**

*K. McCrimmon*

**CONTENTS ix**
**On the Isomorphism Problem for Finite Dimensional Diagram**

**Algebras . . . 955**

*W. D. Burgess andJ.-B. Du*

**S-Pure-Injective Modules over a Commutative Priifer Ring . . . 961**

*M. Prest and G. Puninski*

**New Simple Infinite Dimensional Lie Algebras Related to Those of**

**Generalized Cartan Type H . . . 973**
*V. Jia*