Several types of circular DNA molecules are now known. These are classified as single-stranded rings, covalently closed duplex rings, and weakly bonded duplex rings containing an interruption in one or both strands. Single rings are exemplified by the viral DNA from phiX174 bacteriophage. Duplex rings appear to exist in a twisted configuration in neutral salt solutions at room temperature. Exam...

In this paper, we show that one can construct a \begin{document}$ G $\end{document}-code from group rings is reversible. Specifically, given with subgroup of order half the ambient an element its own inverse outside subgroup, give ordering elements for which id="M4">\begin{document}$ $\end{document}</tex-...

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...

A long-standing conjecture due to Michael Freedman asserts that the 4-dimensional topological surgery conjecture fails for non-abelian free groups, or equivalently that a family of canonical examples of links (the generalized Borromean rings) are not A−B slice. A stronger version of the conjecture, that the Borromean rings are not even weakly A−B slice, where one drops the equivariant aspect of...

In this paper, we give a new method for constructing LCD codes. We employ group rings and well known map that sends ring elements to subring of the n×n matrices obtain Our construction guarantees our codes are also codes, namely, ideals in ring. show with certain condition on element v, one can construct non-trivial Moreover, by adding more constraints reversible. present many examples binary w...

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pro...

In this contribution the problem relating dynamic behavior and parameter values for weakly reversible chemical reaction networks (CRNs) that obey the mass action law is revisited. The approach is founded on previous methods and results discussed in [15, 16] for weakly reversible CRNs. Two new research directions are however undertaken in this study, one of them exploits an alternative factoriza...

It is shown that if R and S are Morita equivalent rings then R has weakly stable range 1 (written as wsr(R) = 1) if and only if S has. Let T be the ring of a Morita context (R,S,M,N,ψ, φ) with zero pairings. If wsr(R) = wsr(S) = 1, we prove that T is a weakly stable ring. A ring R is said to have weakly stable range one if aR + bR = R implies that there exists a y ∈ R such that a + by ∈ R is ri...

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem statement can be traced back at least 30 years ago. The algorithm uses standard linear and mixed integer linear programming, and it is based on elementary graph...

A ring [Formula: see text] is said to be clean if each element of can written as the sum a unit and an idempotent. weakly either or difference idempotent, feebly every text], where are orthogonal idempotents. Clearly, rings both them clean. In recent paper (J. Algebra Appl. 17 (2018) 1850111 (5 pp.)), McGoven characterized when group clean, distinct primes. this paper, we consider more general ...