On Construction of Optimal A2-Codes

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｔｈｅａｕｔｈｅｎｔｉｃａｔｉｏｎｃｏｄｅｓｗｉｔｈａｒｂｉｔｒａｔｉｏｎ (Ａ2 ｃｏｄｅｓ)ａｒｅｉｎｔｒｏｄｕｃｅｄｂｙＳｉｍｍｏｎｓ[1]ａｎｄｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ (ｆｏｒｅｘａｍｐｌｅ ,[1— 8] ) .Ｏｎｅｏｆｔｈｅｍｏｓｔｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｓｉｎｔｈｅｓｔｕｄｙｏｆａｕｔｈｅｎｔｉｃａｔｉｏｎｃｏｄｅｓｉｓｔｏｆｉｎｄｌｏｗｅｒｂｏｕｎｄｓｏｎｃｈｅａｔｉｎｇｐｒｏｂａｂｉｌｉｔｉｅｓａｎｄｏｎｔｈｅｎｕｍｂｅｒｓｏｆｅｎｃｏｄｉ…     

Annihilators in BCK-Algebras

We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\mathcal{A}$ . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice ${\mathcal{D}\left( \mathcal{A} \right)}$ of all deductive systems on $\mathcal{A}$ . Moreover, relative annihilators of ${C \in \mathcal{D}\left( \mathcal{A} \right)}$ with respect to ${B\;{\text{in}}\;\mathcal{D}\left( \mathcal{A} \right)}$ are introduced and serve as relative pseudocomplements of C w.r.t. B in ${\mathcal{D}\left( \mathcal{A} \right)}$ .     

Annihilators of Mal'tsev algebras

Let be an associative ring with 1, containing 1/6,and let A be an arbitrary Mal'tsev -algebra. For some fully invariant ideals of an algebra A, we prove that their products lie in the annihilator Annof this algebra. As a consequence, it is inferred that for every algebra A over a field of characteristic 0, satisfying the nth Engel condition, there exists an N such that .Also, some identities in Mal'tsev algebras having faithful representations are proved to hold in separated Mal'tsev algebras; in the class of alternative algebras, new central and kernel functions are constructed. Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 576–595, September–October, 1994.     

Annihilators of rational modules

We apply the Cauchy transform to derive results which relate approximation problems in different Lipshitz norms, and in the uniform norm, to one another.     

Annihilators for cusp forms of weight 2 and level 4p m

We obtain operators, given essentially by formal sums of Hecke operators, that annihilate spaces of cusp forms of weight 2 for Γ ₁(p ^m )∩Γ(4), whose dimensions will be specified. Moreover, we obtain the principal part (mod p), over the cusps, of certain meromorphic modular functions of level 4p ^m .     

Annihilators in rings with involution

In this paper we examine the annihilators of algebraic expressions in the symmetric, or skew-symmetric, elements of a ringR with involution. LetL be the set of elements ofR each of which is annihilated on the right by some power of each symmetric element. IfR contains no nonzero nil left ideal thenL=0. The subset ofL annihilated by a fixed power of each symmetric element is always a nil left ideal ofR of bounded index. WhenR is an algebra over a fieldF, letA be the left ideal of elements annihilated on the right by some polynomial in each symmetric element. If eitherF is uncountable or the degrees of the polynomials are bounded, thenA generates an algebraic ideal ofR. Similar results are obtained by using skew-symmetric elements instead of symmetric elements.     

Annihilators in Nonrepetitive Semigroups

It is well known that one can construct an infinite sequence on three or more symbols such that no two consecutive blocks are identical. In this paper we give a combinatorial characterization for those finite sequences which are maximal in the sense that appending to them even one more symbol yields two consecutive identical blocks.     

Annihilators, Multipliers and Crossed Modules

Using multiplication algebras we introduce actor crossed modules of commutative algebras and use it to generalise some aspects from commutative algebras to crossed modules of commutative algebras. This is applied to the Peiffer pairings in the Moore complex of a simplicial commutative algebra.     

Annihilators in Normal Autometrized Algebras

The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra is an ideal of and every principal ideal of is an annihilator of . The set of all annihilators of forms a complete lattice. The concept of an I-polar is introduced for every ideal I of . The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of containing I.