In 1987 Tom Head [5] introduced the idea of splicing as a generative mechanism in formal language theory. This mechanism was popularized and extensively developed by Gheorghe Păun and his many coworkers, who recognized much of the subtlety and power of this mechanism and who used it as a foundation for the rapidly developing study of DNA based computing. See, for example, [11] and [12]. (The mo...

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

This is the scientific report for the paper entitled “Yet Another Compiler for Active Security or: Efficient MPC Over Arbitrary Rings”. This research produces a powerful idea for transforming any semi-honestly secure multiparty computation (MPC) into an actively secure protocol while taking into consideration reducing the threshold of tolerance corruption for real parties by semi-honest adversa...

We introduce the "$type{lffs}$ subdirect product" and show that every ring is uniquely a $type{lffs}$ subdirect product of a family of $simple{basicls}$ rings. Also we show some applications.

We show that the odd-indexed derived Witt groups of a semilocal ring with trivial involution vanish. We show that this is wrong when the involution is not trivial and we provide examples.

a simple, mild and efficient method for the regioselective nitration of various aromatic compounds usingpoly(4-vinylpyridinium nitrate) (p4vpyn) in the presence of melamine trisulfonic acid (mtsa), is reported.this method provides several advantages such as good selectiveity between ortho and para positions ofaromatic compounds, clean procedure, simple work-up, short reaction times, solvent-fre...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...