Let R be a RING and V be a MATRIX VALUATION on R. It is shown that, there exists a correspondence between MATRIX VALUATIONs on R and some special subsets Σ(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant VALUATION RINGs and abelian VALUATION functions on a division RING. Furthermore, based on Malcolmson’s localization, an alternative proof for the following result is presented. “There exists a natural bijection between the MATRIX VALUATIONs on R and valuated EPIC R-fields.”

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-VALUATION near RING and Pseudo-VALUATION N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near RING with quotient near-field K and P be a strongly prime ideal of near RING N, then is a strongly prime ideal of , for any multiplication subset S of N. In addition, they obtained the relation between strongly prime ideal and strongly prime N-group, and also between Pseudo-VALUATION near RING and Pseudo-VALUATION N-subgroup. It has also shown that if every N-subgroup be ideal of M and P be a strongly prime N-subgroup of M, then (P: M) is a strongly prime ideal of N. And in the end it is proved that if P and L of N-subgroups M and Psubset of L such that for any y in K , y-1P subset of P, then L is a strongly prime N-subgroup of M if and only if L/p is a strongly prime N-subgroup of M/p.

In this work the notion of a bornological linearly topologized module over a discrete VALUATION RING is introduced and it is shown that certain semimetrizable linearly topologized modules are bornological. The main result is a characterization of bornological linearly topologized modules, from which the completeness and the quasi-completeness of certain linearly topologized modules of continuous linear mappings are derived.

With the growing knowledge of economics, the role of intellectual property in the development of international businesses and the boom of the national economy has become increasingly pronounced. There are many items on the intellectual property list, but the patent may be the most important intellectual property. Patent rights that bRING patent owner immunity are very valuable. These licenses have been tradable in certain markets, like many other economic markets, and one of the concerns of technology researchers has always been to calculate the value of patents and to decide whether or not to buy them. The present study has developed a system for patent VALUATION. In the first step, the decision to invest or not invest in intellectual property (policy making) is examined using Ohlsen's model. In the second step, the patent VALUATION is done by using the real option VALUATION methods.  Implementation of Ohlsen's model in companies listed on the Tehran Stock Exchange has highlighted the importance of advertising as one of the customer-centric intellectual property of the share price. in second step, a patent is valued in terms of the option to assign and simulate future patent cash flows using the average return process.