The sub-semi-groups excluding zero of a near-ring

A Characterization of Left Regularity

“…As we shall see in the next result, condition 3 follows from the other conditions, so when we say that N is an ACN, we mean that N satisfies conditions 1, 2, 4. Anshel-Clay near-rings have been defined in [2], but they occured implicitely in previous papers on planar and strongly uniform near-rings, see for example [3], [4], [5] and [6]. In [2] and in [7] these near-rings have been used to coordinatise certain noncommutative spaces.…”

Cathodic Mapping of Leakage Defects

“…Then the wafer is placed in an electrolyte, an aqueous solution of 8% sulfuric acid, and acts as an anode with an applied voltage of 2.5-5V. If a device has a leakage current above a cer- tain level, the aluminum pads (instead of the silicon) on the device contacts will be oxidized 2A1 + 30 = ~=~ A1208 + 6e [3] This version is a vast improvement qver the two preceding versions, in two respects. First, the high contrast in reflectivity between the unoxidized and the oxidized aluminum pads makes excellent visibility for rapid scanning of leaky units.…”

“…Parameters such as sheet resistance and film thickness have been shown to vary systematically over the surface of a processed silicon wafer (3,4). The equivalue contour maps (topographs), which were used in Ref.…”

The automorphism group of a class of semi-groups

“…is a semigroup because it is closed under .. Since R is finite, so is S. For each r in S, there is a positive integer n depending on r such that r n = r, so r n-1 is the identity of r. Moreover, since r is a left nonzerodivisor, r n-1 is the unique right identity of r. Noting that r n-1 is an idempotent, we have /~----rn-l.R ~-R' such that rn-lR'~-O, and hence R'-~O for r n-1 is in S (see the proof of Lemma 1.2 in [6]). Thus the idempotent r "-1 is a left identity of R. From what has been done, it is easy to show that S is a partition of the subgroups Se~, where {el,e2,...,en; for some integer n}are all different nonzero idcmpotents of/~ such that S e~ ~-S e I by I,l (s e~)----~-se~ej-~se~ for each s in S and i,j-----1,2 ..... n (see the proof of Th.…”

“…Introduction. In [6], the structure and number of sub-semigroups excluding zero of a near-ring were found ( [6], Lem. 1.4, Th.…”