Fuzzy languages and fuzzy automata are considered using techniques from algebraic theory of automata. Syntactic monoids of fuzzy languages play a crucial role in the study. Varieties of fuzzy languages are introduced and an Eilenberg-type correspondence between varieties of fuzzy languages, varieties of ordinary languages and varieties of monoids is established.

The Chow flag varieties are introduced and studied. In a family of pure dimensional projective complex varieties defined via Chow flag varieties, the isomorphism type of Lawson homology of a general member in the family is discussed. Applications to morphic cohomology and motivic cohomology on smooth projective complex varieties are discussed.

We prove that Grothendieck’s Hodge standard conjecture holds for abelian varieties in all characteristics if the Hodge conjecture holds for complex abelian varieties of CM-type, and that it holds for all smooth projective varieties if, in addition, the Tate conjecture holds for smooth projective varieties over finite fields.

The universal algebraic literature is rife with generalisations of discriminator varieties, whereby several investigators have tried to preserve in more general settings as much as possible of their structure theory. Here, we modify the definition of discriminator algebra by having the switching function project onto its third coordinate in case the ordered pair of its first two coordinates bel...

In the present paper we study varieties of linear k-algebras over a commutative associative Noetherian ring k with 1, whose subvarieties form a chain. We describe these varieties in terms of identities in the following cases: residually nilpotent varieties, varieties of alternative, lordan and (1, l)-algebras.

Adults of Rhyzopertha dominica (F.), the lesser grain borer, were exposed on four varieties of rough rice with Dobie indices of susceptibility of 1.1 to 1.1 (low), and four varieties with Dobie indices of susceptibility of 3.4 to 3.8 (high). The varieties with low and high Dobie indices were classified as resistant and susceptible, respectively, to R. dominica. The purpose of the study was to e...

Deligne has shown that there is an equivalence from the category of ordinary abelian varieties over a finite field A: to a category of Z-modules with additional structure. We translate several geometric notions, including that of a polarization, into Deligne's category of Z-modules. We use Deligne's equivalence to characterize the finite group schemes over k that occur as kernels of polarizatio...