The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

A Characterization of Varieties of Associative Algebras of Exponent two

∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.

Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions

* Partially supported by Grant MM-428/94 of MESC.

The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3

Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.

A Basis for Z-Graded Identities of Matrices over Infinite Fields

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50

Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero

2000 Mathematics Subject Classification: 14B05, 32S25.

Moduli stacks of polarized K3 surfaces in mixed characteristic

2000 Mathematics Subject Classification: 14J28, 14D22.

Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

2000 Mathematics Subject Classification: 47A10, 47A13.