A Ring Associated with a Near-Ring

Abstract

Ž. Let N be a right near-ring with identity such that N, q is abelian. Because N enjoys the right distributive property, every right multiplication map on N is an Ž . endomorphism of N, q . The set of all right multiplication maps on N generates Ž . a ring ‫,ޒ‬ a subring of the ring End N . The structure of ‫ޒ‬ is investigated when N is a finite simple near-ring and when N is a finite centralizer near-ring. ᮊ 1996Academic Press, Inc.

Purification and characterization of a low molecular weight multifunctional cytotoxic phospholipase A2 from Russell's viper venom☆

“…The number of residues modified was calculated using ε 367 nm = 11,000 M −1 cm −1 for released trinitrophenyl amino group [24]. Arginine residues were modified by incubating 0.05 mg of RVV-7 in 1 ml of 0.2 M Na-borate, pH 9.8, with 40 mM of 1,2-cyclohexanedione for 3 h at 37 • C [25].…”

Graded near-rings

“…Let A(N ) be the associated ring of N , i.e. the subring of End(N ) generated by P (see [6]). Any element of A(N ) is a finite sum of right multiplication maps from P .…”

Generalized blocked triangular matrix rings associated with finite abelian centralizer near-rings

“…In this section we consider the setting in [13,Section 3]. For the ease of the reader we provide the pertinent results, definitions and notation.…”

“…In [13,Section 4] it was shown that the subring J of V. generated by the set [p[n]: neN with stab(u) c stab(n(u)), VO ^ v e G] is a nilpotent ideal of K, and that H/1 is isomorphic to a direct sum of complete matrix rings, with TZ the right ring associated with N. Consider the set {£,,,..., £"} of orthogonal idempotents in TZ (with sum 1 R ) as in Section 2, and note that if stab(u, m ) g stab(t;, ( ), with 1 < I, m < p, then, as every element of E^iJlZE,^ has the form it follows from (3) that E^JR-E,^ = [0). Furthermore, in this case for all k and k such that 1 < k < t m , 1 < k < t,, since s t a b^J = stab(i>,J g stab(» (| ) = stab(y (u ,).…”

“…(N, +) is abelian. We consider a specific subring of the ring End(N) of endomorphisms of the abelian group (N, +), namely the subring H generated by the set of right multiplication maps p[ri\: N -*• N, with p[n](m) = mn, m,n e N, called the right ring associated with N in [13]. Note that every element of TZ can be written as a (finite) sum £ u p[n u ] of right multiplication maps, with the n u 's elements of N.…”