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According to a result by K. B. Lee, the lattice of varieties of pseudocomplemented distributive lattices is the ui + 1 chain B_i C Bo C Bi C • ■ ■ C Bn C •■ • C Bw in which the first three varieties are formed by trivial, Boolean, and Stone algebras respectively. In the present paper it is shown that any Stone algebra is determined within Bi by its endomorphism monoid, and that there are at mos...

We consider endomorphism monoids of graphs. It is well-known that any monoid can be represented as the endomorphism monoid M of some graph Γ with countably many colors. We give a new proof of this theorem such that the isomorphism between the endomorphism monoid End(Γ) and M is absolute, i.e. End(Γ) ∼= M holds in any generic extension of the given universe of set theory. This is true if and onl...

We construct a simple, nuclear, stably projectionless C∗-algebra W which has trivial Ktheory and a unique tracial state, and we investigate the extent to which W might fit into the hierarchy of strongly self-absorbing C∗-algebras as an analogue of the Cuntz algebra O2. In this context, we show that every nondegenerate endomorphism of W is approximately inner and we construct a tracepreserving e...

In EUROCRYPT 2009, Galbraith, Lin and Scott constructed an efficiently computable endomorphism for a large family of elliptic curves defined over finite fields of large characteristic. They demonstrated that the endomorphism can be used to accelerate scalar multiplication in the elliptic curve cryptosystem based on these curves. In this paper we extend the method to any genus 2 hyperelliptic cu...

The notions of density, thinness, residue and ideal in a free monoid can all be expressed in terms of the infix order. Guided by these definitions we introduce the same notions with respect to arbitrary binary relations. We then investigate properties of these generalized notions and explore the connection to the theory of codes. We show that, under certain assumptions about the relation, densi...

We consider the endomorphism ring computation problem for supersingular elliptic curves, constructive versions of Deuring’s correspondence, and the security of Charles-Goren-Lauter’s cryptographic hash function. We show that constructing Deuring’s correspondence is easy in one direction and equivalent to the endomorphism ring computation problem in the other direction. We also provide a collisi...

A loop (Q; ·) is called a Basarab if the identities: (x · yxρ)(xz) = x yz and (yx) (xλz x) hold. It was shown that left, right middle nuclei of coincide, nucleus set elements whose inner mapping Tx are automorphisms. The generators group were refined in terms one total loop. Necessary su_cient condition(s) (associators) for to be established. discovered loop: ↦ an endomorphism only left (right)...

‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $R$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{sigma,tau}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper‎, ‎it is shown that if charac...